The former shadow cabinet minister Sarah Champion has said she would “take no deal” over remaining in the EU, arguing that Labour had to deliver the result of the referendum.

MPs close to Boris Johnson have suggested they believe his administration could secure enough Labour votes to pass a new version of a Brexit deal, after Jeremy Corbyn said Labour would campaign for remain in a second referendum.

Champion, a former shadow equalities minister who repeatedly voted against Theresa May’s Brexit deal, said she could not support Labour transforming into a remain party.

“If my party comes out as a remain party rather than trying to find a deal or rather than trying to exit, I can’t support that, it goes against democracy,” the MP for Rotherham told BBC Politics Live. “I want us to leave, the country wants us to leave and for our democracy I think we have to leave.”

Champion said it was an “awful question” as to whether she would prefer no deal over no Brexit, but she said: “If it came to it I would take no deal if that meant we could leave.”

Champion appeared to suggest she had thought Labour MPs could get more concessions from May, and this had prevented her from backing the prime minister’s deal.

“It’s poker, isn’t it? And if I’m being completely honest, I hoped she would listen to what the Labour frontbench was saying and move and she didn’t. The extent she moved effectively caused her to be sacked.”

Asked whether she would back the government in a confidence vote in order to deliver a no deal, Champion said: “I don’t know. Ask me closer to the time.”

Several Labour MPs have expressed regret that they did not vote for May’s Brexit deal in March, before the EU’s extension, including Gareth Snell and Stephen Kinnock. “I made a mistake,” Snell told the House of Commons last month. Snell said Labour “will have been responsible for a no-deal Brexit by default because of our inability to make a decision”.

One minister close to Johnson said they believed that if Johnson was confirmed as prime minister he would be more able to bring MPs on board with a new deal. “I don’t think we will get to no deal,” the minister said.

“If Boris is able to bring MPs from all sides of the party on to the campaign, he is more likely to bring people with him to get a deal through. There may now be enough Labour MPs who are ready to end this mess – and sick of Corbyn’s position – in order to pass this.”

Kinnock wrote in the Guardian last month that MPs should have been whipped to back May’s deal, calling it “far from ideal” but calling it “the only feasible means of preventing no deal”.

Labour MPs who are prepared to back a new Brexit deal may not be prepared to vote against their party whip in a confidence vote. A new prime minister’s working majority in the Commons is likely to be reduced to three if the Liberal Democrats win the Brecon and Radnorshire byelection on 1 August.

Two Tory MPs, Dominic Grieve and Kenneth Clarke, have suggested they would be prepared to vote against the government but a number of other MPs’ positions are uncertain.

They include the independent Northern Irish MP Sylvia Hermon and the former Labour MPs Frank Field, Ian Austin and John Woodcock, who are strongly opposed to a Corbyn government.