Foreign Secretary Jeremy Hunt has talked to BBC political editor Laura Kuenssberg about his ambition to be prime minister. Here is the full transcript of their interview.

Laura Kuenssberg: Foreign Secretary. First of all what would you do on day one in Number 10 to get us out of the EU at the end of October?

Jeremy Hunt: Well, we have to approach this differently. It's the biggest constitutional crisis that I can remember, and the key is to put together a negotiating team for Brexit that will demonstrate to the EU that we can deliver parliament. So what I do differently to what we've had before is I would have the DUP in my negotiating team, I'd have the ERG who are the Brexit purists, I'd have the Scottish and Welsh Conservatives, because fundamentally I believe there is a deal to be done.

JH: When I talk to European leaders this is doable. But we have to take the right approach. One of the reasons that they stopped talking to us before was because they didn't think that the British government would deliver the British parliament. That's what we need to change.

LK: But how would you bring those people together? I mean could the negotiating team function when you have people who fundamentally disagree with each other inside it?

JH: Well this is the big difference between the way I want to handle it and the way we handled it before, because yes, I think there is a deal that can unite all wings of the Conservative Party and our friends in the DUP, but it's got to be different to Theresa May's deal. We can't put forward a deal to Brussels unless they absolutely know that it could get through the British parliament.

LK: So what would the deal be, what would be different about the deal you hope to achieve?

JH: Well it would be changing the backstop with some guarantees that we're not going to have a hard border on the island of Ireland for completely obvious reasons. That approach is not too different to what Boris wants. I think it'll be a technology led solution. But we had a lot of discussion about 'how', we need to have a discussion about 'who'. Who is the person that we trust to send to Brussels on behalf of the British people and come back with a deal, and that has to be someone that they trust, that they're prepared to talk to, because in the end you don't do a deal with someone you don't trust. Then it has to be someone who isn't going to blink, who's prepared to walk away if we don't get what we needed. I'm prepared to do absolutely that. But I don't want us to lose hope. There is a deal to be done. You've just got to make sure that we send the right person to get it.

LK: But it is also about how you would do it. You are putting forward, just as Boris Johnson told us yesterday, something that the European Union has said no to on multiple occasions. It's what Theresa May tried and failed to do many times.

JH: Well, what Theresa May tried to do was a deal involving the backstop. I was in cabinet at the time and I supported her loyally but I never thought that was the right approach. What I'm talking about is a deal that doesn't involve the backstop as it's constituted at the moment, so it would be different. And when I talk to European leaders, what they say is 'look, it's up to the UK to come up with a solution'. But of course if you come up with a different solution, something that can work, when we'll look at the whole package.

LK: But what would it be?

JH: Well it will be a technology-led a solution. I think everyone thinks that within the next decade we aren't going to have big border checks when it comes to goods because we're going to do all these things online, just like the rest of our lives is transformed, and that discussion is what do you do if there's a disagreement about what technology can do, so you need some mechanisms that resolve those disputes.

LK: But what happens before then? Because for three years people have been talking about potential technological solutions to the Irish border, and nobody has come up with anything that is convincing at this moment, and that's why the EU has always been crystal clear. You won't have a deal unless there is a backstop, unless there is a credible idea ready immediately. And you're not saying it's ready immediately, you're talking about within a decade.

JH: No I think it is ready…

LK: Now?

JH: Yes I do. But the EU have not wanted to accept this kind of solution because the hope is that we might stay in this thing called the customs union where we have to stick to that tariffs. But I think they know now that won't get through Parliament. So what I'm saying is let's not be negative, let's not be pessimistic. There is a way we can do this but what we have to do is send the right prime minister to Brussels to have those negotiations, have those open discussions and then I think there is a deal to be done.

LK: But you're saying then that the EU didn't want to accept this idea because they wanted to keep us in the institution, one of the institutions, the European Union. That's your contention.

JH: Well I think they've always wanted us to remain as close as possible to the EU, but it's very clear that what people voted for in the general election that we had two years ago it was for us to leave the customs union, leave the single market, and any...

LK: But that's a different point what you're suggesting. Foreign Secretary, is that somehow the EU didn't listen to more creative ideas for the backstop because they wanted to keep us closer?

JH: Well this is a negotiation and they obviously are going to negotiate for what is for them the best outcome. But the reality is we ended up with a deal that's not going to get through Parliament and I think when I talk to people in the EU they understand that, they are keen to see if there's a way through this, and I think the choice for us at this very critical moment is - do we send someone that can negotiate, I'm an entrepreneur by background, I've done negotiations all my life inside government, outside government. And I think there is a deal to be done, but I'm not going to pretend that it's easy. And really it's about taking a smart approach. Yesterday, I was at the Port of Bristol and I was asking the managing director there, what is the art of negotiation? And he said to me you've got to understand what the other side really want. You've got to have a connection with them but you've also got to be prepared to be very very tough and that's what I'd be.

LK: But why would EU leaders want to trust you on this when one of the first things you did as Foreign Secretary was offend half of Europe by comparing the EU to the Soviet Union?

JH: Laura I am not afraid to speak uncomfortable truths to our partners in the EU. The point I made in that speech was it was totally inappropriate for an organisation that was set up to defend freedom to make it impossible for a member to leave. I will say tough things when I need to say tough things. But I'll also preserve the relationship. I think I've also shown as foreign secretary that I can have good links with European countries. And that's why I'm the right person to deliver Brexit.

LK: And how long would you keep trying to get a deal before you decide to walk away? So unlike Boris Johnson you are willing to go beyond the October 31 deadline. But for how long would you keep trying to get a deal before you say okay, this is impossible. Time to go for no deal.

JH: Well I think that 31 October come hell or high water is a fake deadline, because it's more likely to trip us into a general election before we've delivered Brexit, and that would hand the keys to Jeremy Corbyn and then we'd have no Brexit at all. But in my case how would I approach this. I think we'll know very soon well before 31st October. If there is a deal to be done along the basis I've said. If there isn't and if no deal is still on the table I've been very clear. I will leave the European Union without a deal. But I'm not going to do that if there's a prospect of a better deal and if I did it it would be with a heavy heart because businesses up and down the country would face a lot of destruction. I think it'd be very bad for the union, with Scotland where I was at the weekend… so I would do it though. But as a last resort.

LK: But what you're saying though is you would make a decision before October 31 on whether to leave without a deal.

JH: That's correct. And I'm very clear that if we haven't got the prospect of a deal that can through parliament by that date, then that is the option I'll choose.

LK: And who will define that you sitting in the study at Number 10? You make a decision?

JH: Yes. I will make a judgment. But I think to be honest everyone will know at that stage. The question is who is the person that we're going to send to Brussels who can bring back that deal that has a chance of getting through Parliament and I really believe I could.

LK: What's the evidence though that you could? I mean listening to you talking about your Brexit plans is actually very similar to talking to Boris Johnson about his Brexit plans - high on ambition low on concrete detail.

JH: No I've been very clear about the concrete detail. So we've just been talking about the fact that it wouldn't include…

LK: You've been clear about what you'd like to do but it's a wish. What's the evidence you could actually get this done?

JH: Well that is the starting point for any deal, you've got to be absolutely clear about what you want, and it's different from what Theresa May was negotiating. The answer to your question is that both Boris and I want to change that deal, and the judgement is, who is the person we trust as PM to go to Brussels and bring back that deal? It's about the personality of our PM. If you choose someone where there's no trust, there's going to be no negotiation, no deal. And quite possibly a general election which could mean we have no Brexit either. If you choose someone that the other side will talk to who's going to be very tough, there will least be in negotiation and I believe this deal to be done.

LK: And you don't trust Boris Johnson. You don't think he'd be trustworthy as PM…

JH: I would never make those comments about a fellow candidate. I would serve Boris Johnson to the very best of my ability and make his prime ministership a success and I hope he'd do the same for me.

LK: Foreign Secretary you've just sat there in a race of two and said "this is about who we can trust someone we can trust like me or someone we can't trust". You are clearly talking about your opponent in this race, and saying he is not trustworthy enough to become our prime minister.

JH: No I'm saying I am trustworthy and I do believe that I can be trusted to deliver this deal and I've got a background as an entrepreneur, as a negotiator, someone who's done very big complex negotiations like getting the extra 20 billion pounds for the NHS which I did when I was health secretary. But also throughout my life. So I think I can deliver that with that. But obviously members of the Conservative Party need to make their choice about who will come back with that deal.

LK: People are also interested to talk about what else you might want to do if you're lucky enough to win this race. Why would you cut corporation tax as soon as you come into office? We already have one of the lowest tax rates in the whole of the developed world. Is it the right priority?

JH: Well let me tell you the answer that. I want to cut taxes on ordinary people so that people can take more money home at the end of the month. I think there are still people who find it incredibly difficult to pay the rent and I want to help them out. But also having been Health Secretary I am passionate about changing the social care system so people are treated with dignity and respect. And I also want to transform the education system so that we abolish illiteracy. Now that's a big shopping list. And the only way that you can afford all of those things is to fire up the British economy. And as someone who set up their own business I want to help thousands more young people set up their businesses. Let me just give you this one example Laura. We're growing at 1.5% a year at the moment. If we were growing at 3% a year which is the American growth rate, we'd have an extra £20bn to spend on public services or tax cuts. All conservatives want to do both of those things and that's why my first focus is to really grow the economy.

LK: And if we leave with no deal there'll be a giant hole in the British economy. There may well be no growth at all. You want to make that corporation tax cut that'd probably be about £13bn, you want to spend an extra £15bn on defence. You want to spend more money on caring for the elderly. Where are you going to get all that cash from? I mean would you borrow more than Philip Hammond has as Chancellor?

JH: No I will follow a fiscal rule that is very clear that debt will continue to fall as a proportion of GDP over the cycle and we've costed these commitments very very carefully indeed. But let me say this. If you have someone who is an entrepreneur by background who passionately wants to grow our economy, and I think with our top universities, with more tech start-ups, and I was a tech entrepreneur, we could be the world's next Silicon Valley. And if we did that we would have the money to put into fantastic public services.

LK: But you're talking about an if, while making promises to spend tens of billions of pounds worth of the country's money on public services. Now as you say every politician would want to do that...

JH: Well the commitment I've made is to cut corporation tax to Irish levels, 12.5%. And when they made that move a number of years ago their GDP per head was lower than ours. Now it's nearly 50% higher than ours. So this is the way that we fire up the economy, we create the jobs, we get the money for our precious public services like the NHS ,transform our social care system, and find tax cuts. But there is no magic about this. If you don't create the wealth you can't spend it.

LK: Well exactly. There's no magic about it. Because there's no magic about it that would be why some people, perhaps including the chancellor who's trying to get you and Boris Johnson to sign up to a commitment not to be profligate, think because there's no magic you can't just be spraying around spending promises.

JH: Well what's the evidence for what I'm saying? The evidence is that in 2010 we took some very difficult decisions to put the economy back on its feet. We've created since then 1,000 jobs for every single day that we've been in office. And then towards the end of that period I was able to get £20bn for the NHS, the biggest ever increase for the NHS. If you do this the sensible conservative way, if you create the wealth, that's what I want to do. Then you can spend money on those vital public services.

LK: You talk very proudly about your record in the NHS but it was not quite as straightforward as you suggest. I mean the three biggest targets that really matter to people - on A&E, on cancer referral, and on 18 week hospital appointments - those targets under your tenure have not been met since 2015. That matters doesn't it?

JH: Well Laura when I arrived at the NHS I met a young dad, who lost his son a week old because of a mistake made by the NHS. Let me finish this story because it's very important, I want to answer your question. And as a result of that he had to write over 400 letters before the NHS told him what had gone wrong. Now the NHS does an amazing job, but I said I wanted to make the NHS safer. And by the end nearly 3m more patients were using good or outstanding hospitals.

LK: No one would question your commitment to the health service while you were there. But on those three big targets for example, people's experience of what they were getting got worse. Targets were missed. There are now tens of thousands of nursing shortages for example, there are problems in the creaking health service that come from the time when you were in charge.

JH: Let me address those. Every single disease category, whether cancer, stroke, heart attack, any other category, outcomes were better when I left the health service compared to when I arrived. The targets you talked about are because of the pressures of an aging population and the only way you can deal with that is by increasing the capacity of the NHS, and what I did as Health Secretary was one of the biggest ever increases in doctor and nurse training places and also that huge increase in funding which meant that the NHS is getting the capacity to deal with those pressures.

LK: And of course you know very well the other big part of that jigsaw is care for the elderly. Now you've admitted the government should have done more on social care, but what would you actually do as Prime Minister? Because this government of which you have been part has been talking about trying to fix social care for years and nothing has happened. We're still waiting for a green paper which is only the beginning of something. What would you do?

JH: Well I negotiated a ten year plan for the NHS, and my next job if I'd stayed as Health Secretary was to a 10 year plan for the social care system, and I do think that councils need more money because I think we want to be a country where we know that as people get older they're going to be properly looked after. So I think there is a bit of public money. But it's also about personal responsibility. I think we should be a country where people save for their social care costs, particularly those last few months, possibly years of their life when things can be very uncomfortable, very painful. Just in the same way they save for their pension. I think it should be something that people can opt out of but it should be an automatic thing.

LK: And would you put a cap on social care costs. I mean on a specific issue lots people have been very worried about this. Theresa May come a cropper on that particular policy. But would you put a cap on social current costs and at what level if so?

JH: I'd do a deal. If you're prepared to save responsibly during your life then we will cut those costs. Do the right thing we need to be a country which rewards people who do the right thing, and I think if we do that, if you look at where we were in the post-war period where many people didn't save for their pensions, we've created a society where the majority of people do save for their pensions. That's the change we need for social care.

LK: OK a couple more brief questions if we may I know we're short on time. You have said that you wouldn't try to change the law to cut the time limit on abortion but also it's the case that MPs tend to put forward this legislation. If an MP put forward legislation to cut the time limit on abortion would you vote to do that?

JH: Well how I voted before is a matter of public record. As you say I've be very clear that as Prime Minister I wouldn't seek to change the law. I didn't as health secretary either. How I vote in any future private member's bill would be a matter of conscience and I would have to see what that bill is before I make that decision.

LK: So you might vote to cut the time limit on abortion?

JH: Well I'd have to look at what that bill was but I think for people watching this programme, what they want to know is as PM I recognise this is a free vote matter and I wouldn't seek to change the law.

LK: Do you understand for some people that is quite worrying. There are many conditions, life limiting conditions that aren't picked up in medical testing until much later in pregnancy for some women. Hearing you say that of course it's a matter of conscience. That is something that feels to them backward looking, not progressive, not understanding.

JH: People have very strong views on all sides on these issues, all I would say is that as Health Secretary I upheld the will of Parliament I didn't seeks to change the law. But I was very honest with people about how I voted, that is a matter of public record, and it would be the same as Prime Minister.

LK: And just final question. Can you actually imagine yourself standing on the steps of Number 10 as prime minister rather than as a cabinet minister beetling in and out for meetings. Do you worry in this contest that you might be somehow unfairly squeezed out by someone with a bigger personality?

JH: Laura I have been waiting for this moment for 30 years of my life. I have been sitting around that table thinking about how I want to transform our country. I think the secret to our amazing country, my dad always said this is the greatest country on the planet. But the secret to our country is we're so entrepreneurial, so dynamic, but we're also compassionate people. We want to have a great NHS, a great social care system, a great education system. I think this is a moment when I look at Brexit and this incredible moment in our history and we could really unleash our potential, and that's what really gets me up in the morning.

LK: You've wanted to be a prime minister for 30 years. When did you know?!

JH: I won't say that. I think if I say that, that's really going to put people off! But… I think 30 years is a very, very long time and this is Britain - but, look, I would love to do this job, I think I can make a difference. I think this is a moment where if we send the right person we can't just solve Brexit, but we can open a whole new chapter in our history, an exciting chapter, and that's what I want to do.

LK: Thank you very much Jeremy Hunt.

JH: Thank you.