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Boris Johnson - the favourite to become next Conservative leader and prime minister - has spoken exclusively to BBC political editor Laura Kuenssberg. Here is the full transcript of their interview.

Laura Kuenssberg: So Boris Johnson what would you do on day one in Number 10 to make sure we leave the EU at Halloween?

Boris Johnson: I would make sure that we have a plan that will convince our European friends and partners that we are absolutely serious about coming out and the key things that you got to do are to take the bits of the current withdrawal agreement, which is dead, take the bits that are serviceable and get them done. And that is number one.

The stuff about European Union citizens, the 3.2 million, they need to be properly protected. I wanted that done the day after the referendum, you may remember. Their rights should be enshrined in an unconditional way in UK law, number one.

Number two, you should look at the various other things that you could do to make progress with the bits of the withdrawal agreement that we have. I think the money is more difficult. I think the £39bn is at the upper end of the EU's expectations, but there is it, it's a considerable sum. I think there should be creative ambiguity about when and how that gets paid over.

The important thing is that there should be an agreement that the solution of the border questions, the Irish border, the Northern Irish border questions, and all the facilitation that we want to produce, to get that done. All those issues need to be tackled on the other side of 31 October during what's called the implementation period.

LK: But the implementation period, as it stands, is part of the withdrawal agreement and you've said that you wouldn't sign up to the withdrawal agreement and it's dead. Those two things can't both be true.

BJ: No, because you're going to need some kind of agreement and that's certainly what I'm aiming for in order, as you rightly say Laura, to get an implementation period. And I think, actually, that politics has changed so much since 29 March. I think on both sides of the Channel there's a really different understanding of what is needed. And on our side of the Channel we've got MPs in both the major parties who recognise that their parties face real danger of extinction at the polls and - you know - Labour went backwards in the recent council elections - unless we get Brexit over the line. And so I think there's going to be a willingness to move this thing forward.

LK: But what is it…?

BJ: On the other side of the Channel, obviously, where you know they're watching this very carefully and we need obviously for both sides to come together, they've not got 29 Brexit MEPs in Strasbourg. They have the £39bn that they're they're keen to get. And, frankly, they also want Brexit to be done.

LK: They want it done in the EU, but they do not want it done at any cost. And time and again whether it is Jean-Claude Juncker, President Macron, any EU leaders, they have been crystal clear. There is no kind of deal without the backstop, an insurance policy for Northern Ireland. So what evidence do you have you can get around that?

BJ: Because I think that it is what the gentlemen have also said and what people have also said in all European capitals - and of course, in the [European] Commission - is that nobody wants a hard border in Northern Ireland and indeed nobody believes that it will be necessary. And so what we need is to hold that thought, which is true, which is agreed amongst all.

LK: It's what people want, but that's very different to want people get, Boris Johnson.

BJ: And make sure that we reach the solutions the are achievable as both sides have said, as the Commission has said. The facilitations that can be reached, make sure that we deal with the solutions to the Irish border question and any other border questions because the Irish border question in microcosm stands for all the other facilitations that we'll around the EU.

LK: But how do you do that? Because you're right - everybody wants a solution to this. But if you want to be prime minister you have to tell people how, you can't just wish it to be true.

BJ: Let me tell you, there are abundant, abundant technical fixes that can be introduced to make sure that you don't have to have checks at the border. That's the crucial thing. And everybody accepts that there are ways you can check for the rules of origin, there are ways you can check for compliance with EU goods and standards, of our goods standards.

LK: But they don't exist yet.

BJ: Well, they do actually, in very large measure they do. You have trusted trader schemes, all sorts of schemes that you could put in to place.

LK: But as one big solution to the Irish border question which as you suggest is absolutely at the root of this, there is no solution ready right now.

BJ: You're right, Laura, that there's no single magic bullet. But there is a wealth of experience, a wealth of solutions. And what's changed now is that there is a real positive energy about getting it done.

LK: Where's your evidence for that?

BJ: Well, because I think on both sides of the Channel there's an understanding that we have to come out, but clearly Parliament has voted three times against the backstop arrangements that you rightly describe. And at present the UK, and any UK government, with this appalling choice of either being run by the EU whilst being outside the EU, which is plainly unacceptable, or else giving up control of the government in Northern Ireland. There is a way forward which I think, actually, to be fair all the candidates in the Conservative Party leadership contest broadly endorsed, which was to change the backstop, get rid of the backstop, in order to allow us to come out without this withdrawal agreement, and as far as I understand the matter, that is also the position of my remaining opponent.

LK: But Boris Johnson, everybody wants this to be sorted. Of course they do. Not least the public. But what you're basically saying is 'we'll cross our fingers because I think the situation is different so we could get a deal done.' You're not giving us anything concrete that actually suggests it's possible.

BJ: No that's not true at all, actually Laura.

LK: Well where's your evidence?

BJ: There was a very good report just today by Shanker Singham and many others looking at the modalities of how to do this. This is something that had been worked on extensively for the last three years. There are plenty of checks that you can do away from the border if you had to do them without any kind of hard infrastructure at the Northern Ireland frontier.

LK: But do you accept that your plan would require agreement from the European Union, political goodwill, and why do you think they would do that when if the UK had just walked away from a deal that has taken them three years to put together?

BJ: Several reasons. First of all, don't forget, that as I say they got the Brexit MEPs they don't particularly want. They want us out, they've got the incentive of the money. They've also got to understand, Laura, is what has changed and what will be so different is that the intellectual capital that had been invested in the whole backstop had really come from the UK side. We were committed to it. We actually helped to invent it. We were the authors of our own incarceration. Take that away. Change the approach of the UK negotiators and you have a very different outcome.

LK: And if you can't do that?

BJ: And simultaneously of course, and you know what I'm going to say, the other tool, the other tool of negotiation that you should use, not only the incentives of getting this thing done, moving it over the line, getting the money across and all the rest, but you have the extra incentive of course that the UK will be ready to come out as you know on WTO terms.

LK: And if you cannot get the agreement that sounds like you're crossing your fingers, you are clear we would leave you would take us out at Halloween without a deal an absolute guarantee?

BJ: You have to be, of course, my pledge is to come out of the EU at Halloween on 31 October. And the way to get our friends and partners to understand how serious we are is finally, I'm afraid, to abandon the defeatism and negativity that has enfolded us in a great cloud for so long and to prepare confidently and seriously for a WTO or no deal outcome.

You've got to understand, Laura, listening to what I just said, that is not where I want us to end up. It is not where I believe for a moment we will end up. But in order to get the result that we want, in order to get the deal we need, the commonsensical protraction of the existing arrangements until such time as we have completed the free trade deal between us and the EU that will be so beneficial to both sides. The commonsensical thing to do is to prepare for a WTO exit.

LK: But unless you can get that deal...

BJ: Now as it happens, by 29 March, a huge amount of work had been done and we had made great progress. There is still as you know some areas that need to be completed some things actually where the kind of level of preparedness is slightly sunk back again.

LK: And Boris Johnson are you, would you really be willing as prime minister to face the consequences of no deal which could mean crippling tariffs on some businesses? It could mean huge uncertainty over what on earth happens at the Northern Irish border. It could mean huge uncertainty for people's livelihoods and people's real lives. Now in the real world, as prime minister and I know you dispute how bad it would be, but are you willing to face the consequences of what a no deal might mean for the people of this country?

BJ: In the real world, the UK government is never going to impose checks or a hard border of any kind in Northern Ireland. That's just number one. Number two in the real world the UK government is not going to want to impose tariffs on goods coming into the UK.

LK: But it's not just up to the UK…

BJ: Hang on, I'm coming to that point…

LK: ... not just up to the UK?

BJ: Of course that's right Laura. It's not just up to us, it's up to the other side as well. And there is an element of course, a very important element of mutuality and co-operation in this. And we will be working with our friends and partners to make sure that we have an outcome that is manifestly in the interests of people, of businesses, communities on both sides of the channel.

LK: And you think you could get that through Parliament?

BJ: I do

LK: You think you could get a no deal through Parliament?

BJ: Well I do. I mean you've got to be very clear. I think Parliament now understands. That the British people want us to come out and to honour the mandate that they gave us. And I think that MPs on both sides of the House also understand that they will face mortal retribution from the electorate unless we get on and do it. Again, what has changed since 29 March is that my beloved party is down at 17 points in the polls. Labour isn't doing much better as I say with superhuman incompetence Corbyn managed to go backwards in the recent council elections.

People want to get this thing done. They want to get it done sensibly. They want to get it done in a way that is generous to European Union citizens in our country and I stress that is the first thing to do. And they want to get it done in a way that allows us to move on which is why I think people are yearning, their yearning for this great Incubus to be pitchforked off the back of British politics. They want us to get on with some fantastic things for this country. And that is what we want to do.

LK: OK, well let's move on because there are plenty of things we want to talk on. So let's move on. Can you just tell us what happened at your partner's home a couple of nights ago?

BJ: I... would love to tell you about all sorts of things Laura, but I've made it a rule over many, many years and I think you've interviewed me loads of times, I do not talk about stuff involving my family, my loved ones. And there's a very good reason for that. That is that, if you do, you drag them into things that, really, is, in a way that is not fair on them.

LK: But now you hope to be in Number 10, things are changing. Does your privacy mean more to you than the public's ability to trust you? Because part of trust is being open, it's being accountable, it's being transparent.

BJ: Yes I get that, I totally get that. But my key point though is that the minute you start talking about your family or your loved ones, you involve them in a debate that is it is simply unfair on them.

LK: But you seem to care about privacy, but you seem to care about your privacy so much that yesterday a photographer, or someone with a phone, just happened to stumble upon you in the middle of the Sussex countryside. I mean are you just trying to have this both ways?

BJ: Look, I repeat my my key point too which is that over many, many years, and you can look back at innumerable statements I gave when I was mayor, I just do not go into this stuff, and there's a good reason for it. But it's actually I think what people want to know is what is going on with this guy? Does he, does he, when it comes to trust, when it comes to character, all those things, does he deliver what he says he's going to deliver? And that is the key thing.

LK: Well let's look at your record then, let's look at that then. Because there are plenty of people even in the Conservative Party who worry that you do not stick to what you promise.

BJ: Well I think they're talking absolute nonsense. When I was mayor, when I became Mayor of London, when we said we would do something, we, I may say delivered not just x, but x plus 10.

LK: But you said you would keep all ticket offices, you closed every single one. You said that you would build more affordable houses - yes, you built more houses…

BJ: We did

LK: ... but the definition of affordable housing changed.

BJ: Oh, nonsense.

LK: You said you've done rough sleeping and the number went up.

BJ: We built more affordable homes than under Labour. When you talk about the Tube we increased capacity on the Tube by about 30%. The biggest investment in infrastructure that I think the city has seen. I pledged to reduce crime. We reduced crime by about 20%. We reduced the murder rate which is a statistic that is very difficult to fudge, we reduced it by 50%.

LK: Then why do you think then, Boris Johnson, people worry about your character? Why do so many Conservatives worry about you sticking to your word or being careless with the truth? I mean you said only a few weeks ago, you would raise tax for the wealthiest in society then that became an ambition.

BJ: Hang on…

LK: You said you'd lie down in front of bulldozers at Heathrow and now you're wobbling. Most importantly, when it came to the British citizen Nazanin Zaghari-Radcliffe you put her in danger by being careless with the facts. Your words were used in evidence against her in an Iranian court. I think you've sometimes been careless with facts, careless with the truth.

BJ: No, look. Take Nazanin Zaghari-Radcliffe and the other very difficult consular cases that we have with Iran. I think, of course, people will want to point the finger of blame at me if they possibly can, but actually all that does is serve to exculpate, lift the blame of the people who are really responsible, who are the Iranian Revolutionary Guard. And if you look, talk about overachieving in the Foreign Office, we were told that we had to orchestrate, and we did, an international response to the poisonings by Russia in Salisbury, and we thought we would be lucky to get 30 Russian spies expelled around the world in support of the UK by other countries. We actually got 153 spies expelled around the world, I don't think there's ever been a diplomatic coup like.

LK: But Boris Johnson...

BJ: So don't look at what people say about me look at what I actually deliver.

LK: But so often people worry that you're just a bit scrappy with the truth, or [it] almost seems, sometimes, you enjoy offending people.

BJ: No, I don't enjoy offending people.

LK: If you are prime minister do you think it would be acceptable for a prime minister to say things like Muslim women in full veil look like bank robbers, or Commonwealth citizens are "flag-waving picanninies"? Do you think, if you move in to Number 10, will you change? If you're lucky enough to become prime minister, will you be a different kind of politician?

BJ: What I pledge to, you know, and what I think the people of this country want to hear, is I will be a politician who sticks by what I believe in. Yes, occasionally I may say things as I've said before that, causes offence, and I'm sorry for the offence and I'm sorry for the offence I caused, but I will continue to speak my mind because I think people deserve to hear what's going on in my head. They deserve to hear my approach to things.

And you talk about my commitment to delivery. Actually look at the difficult things that I've taken on and and done. Nobody thought we could win in London either in 2008 let alone in 2012 when the Tory Party was actually 17 points behind in the polls and I overhauled that deficit. Nobody thought we could win the European Union referendum in 2016. And I played a role with others in getting that over the line.

LK: Why is it then do you think some people have doubts about you?

BJ: By the way, nobody thought the Olympic Games would be a huge success, and the Paralympic Games. I remember people writing them off, I remember people saying it was all going to be a fiasco. And they were a fantastic success.

LK: We're just, we're very much running out of time.

BJ: And if I have one message, forgive me, but I believe that we had amazing success when I was Mayor of London in using infrastructure, education, technology and bringing the greatest city on earth together and lifting people up across the city, closing the opportunity gap in London, giving people tools, whether it's better transport, better education, to take advantage of all the incredible things going on in this city. When I began we had four of the six poorest boroughs in London in the UK. After two terms, when I ended in London, there were none of the poorest 20 boroughs in the whole of the UK. The whole city came up and it was people on the lowest incomes who'd been helped by, by our living wage, who'd been helped by massive investment in public transport, who'd been helped by better education. It was they whose life expectancy had gone up the fastest and whose wealth had also increase. And I'm incredibly proud of that, incredibly proud of that.

And what I want to do now, if I possibly can, and if I'm successful in this contest, and become leader and prime minister, what I really want to do is to bring our country together which has felt divided, which has felt a bit directionless, which has I think because of the failures of the political class, lost a sense of purpose and lost perhaps a bit of a sense of self belief. I want to bring this incredible country together to release the potential of the whole of the UK. That's what I want to do.

LK: Just one of the other people who was very closely involved in the Olympics, of course, was your opponent Jeremy Hunt. What do you make of Jeremy Hunt?.

BJ: And I pay tribute to Jeremy and enjoyed working with him then as I enjoyed working with him in government and who knows, look forward to working with him in the future.

LK: What do you make of him? Today he's saying you're a coward.

BJ: Look, you know I just always invoke the 11th commandment of Ronald Reagan which is "thou shalt never speak ill of a fellow Conservative". And you know what I want to do is talk about my basic message which is to unite our country, bring the country together. Brexit was partly about objection to the one-way ratchet of European Union and democracy. Yes of course it was partly about immigration, but it was about huge parts of Britain feeling that they didn't have the same advantages, the same care, the same love, as London and the southeast, and that they were being a bit left behind. Well, that's an economic mistake. It's a political and it's a social mistake. We need to bring the country together. Infrastructure, education, technology. Give everybody the chance they deserve.

LK: And you really think you can do that when some people see you as the most divisive politician?

BJ: Believe me they said that in 2008 before I became Mayor of London. The Guardian - highly reputable newspaper - ran a whole subsection in which people promised to flee the land or at least the city if I became mayor, eight years later most of them were still there. Many of them had gone to work with me and I had higher approval ratings by far when I left my office as mayor than when I began. And I ran London, yes of course, I believe in the democracy of our country and yes of course we are going to get Brexit done by 31 October.

But be [in] no doubt that at heart I am a centre-right progressive modern Conservative and I will govern from the centre right because that is from the centre because that is where you win. That is where the broad mass of the people are. They understand that you need a dynamic market economy to pay for fantastic public services and infrastructure. And you need fantastic public services and infrastructure, great NHS, great education, to enable business to have the confidence to invest. And Jeremy Corbyn only understands one half of that. He's only interested in taxation and spending. He has no care, no love, no interest for business and for the wealth creators on whom we all depend. And you've got to have that balance in your government.

LK: Well, we will see, if before too long, you'll be able to make that case to him across the despatch box.

BJ: Thank you.

LK: Thanks very much. Thank you very much indeed.