Media playback is unsupported on your device Media caption Boris Johnson talking to Laura Kuenssberg

Boris Johnson spoke to the BBC's political editor Laura Kuenssberg about Brexit, borders and his personal behaviour during the Conservatives conference in Manchester.

Here is the full transcript of the interview.

Laura Kuenssberg: Prime Minister, in the last few weeks, you've lost major votes in the Commons, you've chucked some MPs out of your own party, the highest court in the land has found you broke the law and gave the wrong advice to the Queen. How do you think this is going?

Prime Minister: Well, I think that it's going about as well as could be, especially, if not slightly better.

LK: Really?

PM: Yeah. Because look, this was always going to be a very difficult time. What we've got, basically, is a situation in which the people voted for leaving the EU in the greatest expression of popular will in favour of any party or proposition in history. And, yes, there are many people in all sorts of positions, who don't think that was the right way to go. And I am tasked with getting it over the line, getting Brexit done by October 31. And I think we always knew that as we came up to that deadline, things would get choppy, but...

LK: You are blaming all of your woes on people who are trying to stop Brexit?

PM: No, I think it's just the just the predicament, is just the it's just the situation, that we're in as a country. And I think that things are actually much much better than they, than the political situation, might lead you to believe. Unemployment is at record lows. Foreign direct investment is at record highs. We're seeing this country at the cutting edge of innovation in everything from battery technology to bio science, we are doing fantastically well in so many ways. And if only we could all come together, get Brexit over the line, I think that fevers would cool, tempers would come down. And it would be a great thing.

LK: But you're suggesting that people ought to come together, when transparently, you have been trying to create this idea of them and us, you who want to get Brexit done, which you said every possible opportunity. And the people on the other side, which you've just suggested, are only trying to hold you up and stop Brexit. And that's transparent, you're trying to create a situation of them and us are you not?

PM: I think that the truth is, there's no way of getting Brexit done without, as it were, displeasing people who don't want Brexit to get done - no way of delivering Brexit, sort of 52% Brexit and 48% Remain, that's just logically impossible. And so that I think is, is the problem. But I think once we get it done, and once we can begin building a new partnership with our new friends, once we can start thinking about how we can do things differently, how we can interact with the rest of the world, how we can recover on our impetus, our mojos, as a global outward looking... I think things will will go really well for us. And they already are going very well for us.

LK: But as things stand, are you prime minister sitting there and saying that the last couple of months is anything like a normal situation?

PM: No, because obviously what the UK is going through is a big constitutional change. The extrication, after 45 years of our legal system, from the orbit of European law, which is you know, has become very, very pervasive. It's a very complicated thing to do. And the most complex thing is clearly trying to unravel our relationship with the EU customs union and the EU single market, and the empire of the EU law as it were.

LK: Let's talk about that. So let's be completely clear, under the proposals that you were about to take to Brussels, there would be extra checks on the island of Ireland, how and where?

PM: Well, I mean, if I made the the proposals are not yet made, I probably ought to make them to the EU...

LK: But you know there are suggestions of what is out there, which you deny. So how would you describe what you will put forward?

PM: What I can say is that, and I think this is crucial for everybody to understand, because it's just the limit of what a sovereign country can can do. If the EU is going to insist on customs checks as we come out as it as it is, then we will have to accept that reality. And there will have to be a system, for customs checks away from the border. Now, we think those checks can be absolutely minimal and non-intrusive and won't involve new infrastructure. But that is absolutely, Laura, that is where the argument is going to be. And that's where the negotiation will be will be tough

LK: To be really clear about that. It wouldn't be the EU insisting on checks happening somewhere. If we are in two different economic systems, Of course, there would have to be checks. And that seems to be, the idea of that seems to be toxic to a lot of people. So isn't this just you putting forward similar proposals to what have been suggested that been turned down so many times?

PM: Well, let's see where we get to. And as you know, we made some very constructive and far-reaching proposals...

LK: ... that you haven't published them?

PM: Well, well, we actually the I think that they're quite widely known to minimise the checks for agri-foods for cattle for food. So that stuff moving around the island of Ireland doesn't need to have any checks at all. And that's a huge volume of the north-south trade. Just to set this in context for you this argument, it's important to understand that trade north-south of the border, is dwarfed by trade east-west, i.e. from Northern Ireland to GB. So it would be wrong to, as it were, to create a series of custom to keep Northern Ireland in a customs union with the EU and to create new checks down the Irish Sea for customs....

LK: So you are ruling out checks in the Irish Sea, because that is something that has done the rounds as an idea every now and again.

PM: Well, there already are some checks, as you know,

LK: But extra new checks?

PM: That is epidemiological purposes. Insofar as we've made, I mean, we're really getting into the weeds now. But insofar as we've made it, far as we've made a big move on sanitary, which we have, then that will logically imply some more checks down the Irish Sea. But we think that's liveable with provided it's done in the right way.

LK: If there isn't a deal whose fault will it be?

PM: Well, I'm, you know, I don't want to get into a blame game. But I think that the UK has really moved a long, long way. And what I think we can do, is we can sort out the issue of the UK leaving the EU whole and entire. We can protect the Good Friday process. We can protect the peace process in, in, in Northern Ireland. We can ensure that there aren't checks at the border, no physical, no interruption of trade or movement of people. Absolutely not. And we can also protect the benefits that Ireland has got over the years from the EU single market.

LK: But given the scepticism and concern on the other side about what they've heard so far from your government repeatedly saying it does not go nearly far enough. You really believe that what you're about to put on the table could win the EU round? You do?

PM: Yes, I absolutely do. Yes. And I urge you, Laura to keep hope alive and not, to not, listen...

LK: This is not about people feeling hopeful. This is about whether or not the government can come up with a deal with the European Union, to protect the economy to protect people's jobs and livelihoods. This is not about telling people to cheer up, this couldn't be more serious.

PM: I know. But it's also a question of getting Brexit done by October 31. And doing it in a way that protects the unity and integrity of the United Kingdom. And we are entitled to protect our customs union, and we are entitled to exit as a sovereign state. And, and we can do it in such a way as to preserve the, as I said, all those benefits that Ireland has. So with great, with great respect to, to all those who are currently anxious about it, and particularly in in Ireland, we do think that our proposals are good and creative. But but I accept also, Laura, that, you know, there may be hard yards ahead.

LK: And if we end up, contrary to what you desire, still in the European Union after October 31, you said that the UK would be truculent, suggesting that somehow we would not be a co-operative friend and partner to the EU. What would you do, play rough?

PM: Well... (sighs) I... it goes without saying that the UK would be held against the will of its government and indeed against the will of the of the people of the UK who'd voted to leave. And I think that would be a very unhappy and unfortunate situation. I don't think that is where our EU friends and partners want us to be. So I'm hopeful that we'll get a deal. I'm sorry to sound hopeful. But I think I feel, I'm sorry, if you think that hope is not called for these circumstances. But I do think there is a good chance, gonna put it no higher than that, but a good chance of getting a deal. And we're going to work very hard to do that.

LK: Now you have also this week had to deal with allegations about your own behaviour in the past. And yesterday, you denied that you touched a women inappropriately at lunch, she said you did, is she lying?

PM: I don't want to minimise the importance of this issue or people's concerns about this kind of thing. But in this case, it is simply not true.

LK: So she is lying?

PM: Look, I'm not going to go into whatever when people make these kinds of, of allegations and always be taken very, very seriously. But in this case, it is not true.

LK: Do you remember the event in question?

PM: There is not much more I can say.

LK: Do you remember the event in question?

PM: There is not much more I can say. It is not true.

LK: Well, if there is, because also some people would think in this kind of situation, there should be some kind of investigation, questions should be asked. Should people try to find out what happened because we have completely a "he says, she says" situation here?

PM: I can tell you it is not true. And what I want to do is get on with delivering on what I think is the, I must say, important issue of our domestic agenda, getting not just getting Brexit done, but...

LK: But shouldn't this be cleared up somehow? I mean, you hold the highest political office in the land, this allegation has not been retracted. You yourself wrote almost a year ago, "to all those who worry if we might be a teensy bit unfair on the male sex, I say forget it, put a sock in it. We need that feminist rage." You wrote that these kinds of allegations should be taken seriously.

PM: They should be. But I'm just telling you, I'm just telling Laura, that there's not much more I can say about this issue. Since I've said it several times. But what I can say is that we are focused on delivering on our domestic agenda, I'm very proud of what we're doing on the living wage, which is a massive expansion of the living wage. Taking huge numbers of people out of low pay, effectively abolishing low pay over time and will take the living wage down to people who will receive it at 21...

LK: But do you worry about what female voters think of you?

PM: Yes, of course, Of course. And I think that these are important issues. But I can't really can't give you any more on that subject than what I've already said. Perhaps I could I could remind you that when I, when you ask about, about female voters, we are doing. When I was running in London, we had an administration that was very, very largely women-led and I was very proud of that. We have large numbers of women in the cabinet today. I think we're as many as that are that has ever been. Home secretary, business secretary and so on. And we're very, very, very proud of that. And when I was foreign secretary, my signature policy, most important thing we did was to campaign for 12 years of quality education for every girl in the world. That's a fantastic thing to...

LK: Finally... is the job harder than you thought it might be?

PM: It's a wonderful job. And I...

LK: Wasn't my question. Is it harder than you thought it might be?

PM: Well, I don't want to sound... I don't want to, it's, it's a, it's a, it's a wonderful job. It's a yes, it's a hard job. But I think that every day we are making progress. And I think we can get Brexit done. And I think we can get the country to... I know we can get Brexit done. I think we can get the country to focus on what we're trying to do for people who care about the NHS, for people who care about their kids' education for people who want to see the opportunity extended across this country through infrastructure, education and technology. I think this is going to be a fantastic government and we want to get on and deliver for the people of this country.

LK: Thank you very much.