Theresa May has refused to rule out resigning if her Brexit deal fails to gain approval in the Commons, saying she is focused on persuading MPs that the country supports the deal.

During a public phone-in on BBC Radio 5Live, the prime minister was asked three times to clarify whether she would stake her premiership on the result of the parliamentary vote.

“I’m not thinking about me,” she said. “I’m thinking about getting a deal through that is good for the country. My focus is on getting this deal through.”

May has previously said there was a threat of “no deal or no Brexit” if MPs failed to vote in favour of the deal.

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“Personally, there’s no question of no Brexit, because the government needs to deliver on what people voted for in the referendum in 2016,” she said.

May suggested MPs could change their mind if they listened to the mood of the country.

“In a sense, I think there’s two conversations going on at the moment,” she said. “In parliament there’s a lot of focus on who’s going to vote for the deal or not, and outside I think people are thinking: ‘Actually, let’s make sure we can get this through and get on with delivering’.

“My job is to persuade people. I believe this is the right deal for the UK. My job is to persuade people in parliament of that view,” she said. “And I think the job of an MP is actually, when they come to look at voting for this deal, to say to themselves, ‘Does it deliver on what people voted for?’ – I believe it does – and secondly, ‘What do we need to focus on for our constituents, for people up and down the country?’”

May’s spokeswoman told journalists earlier on Friday that cabinet ministers would be engaging widely with the electorate in the coming days, with Philip Hammond and Liam Fox visiting Northern Ireland.

May rejected the idea that a better deal could be secured through further negotiation. “If this deal doesn’t go through we are back at square one. What we end up with is more uncertainty and more division.

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“I believe that if we were to go back to the European Union and say: ‘People didn’t like that deal, can we have another one?’ I don’t think they are going to come to us and say: ‘We will give you a better deal.’ This is the deal that I think works for the UK.”

May was also asked whether she truly believed the UK would be better off outside the EU. She said the end of free movement and ending annual payments to the EU were examples of ways the country could be better off.

“I think we will be better off in a situation outside the EU where we have control of all of those things and are able to trade around the world,” she said.

In answer to one caller, May admitted the Brexit negotiations were keeping her up past midnight most nights, but if the deal was passed she would celebrate with her husband, Philip. “We will have a drink together.”