The former Brexit secretary Dominic Raab has vowed to vote against Theresa May’s withdrawal agreement unless the EU accepts “substantive, legally binding changes”.

He also accused the EU of behaving “dishonourably” by using sensitivities around Northern Ireland as a bargaining chip in its negotiations with the UK.

Raab’s interview with BBC Radio 4’s Today programme underlines the challenge facing the prime minister in overcoming the continued hostility in her party to her deal.

Raab said he did not accept the “Faustian bargain” of backing May’s deal to avoid the risk of staying in the EU.

Asked if he would vote against the deal as it stands, Raab said: “It needs to change. We need to see substantial, substantive legally binding changes to the withdrawal agreement. The most obvious specific change is the ability to exit the backstop, whether through a sunset or timeframe or a mechanism that allows us to be confident that we go into the end of 2021 knowing we are free of the backstop.”

He added: “If we sign this deal as is with no change, the problems will get worse and we will go into the next election, potentially, stuck in the backstop begging the EU to let us out of it and not having delivered on our promises to the voters, and I think that would be devastating for public trust in our democracy.”

Earlier this week, Jacob Rees-Mogg, the chairman of the hardline pro-Brxit European Research Group, suggested he was prepared to soften his objection to the deal by saying he would accept a change in the form of a codicil to the agreement.

Raab denied the Brexiters were changing tack. He said: “I don’t think there has been any change in Jacob’s position. The point is we are not being dogmatic about this, on the Brexiteers’ side, we want to see the substance of it changed but the vehicle, the technical device for doing it is second order; what matters is that we can exit that backstop so that we do not as a country sign up to a whole regime of laws from economy to social policy, over which we have no control and no means of exit.”

Raab expressed support for George Eustice, who resigned as agriculture minister on Thursday in protest at May’s decision to allow a vote on delaying article 50.

He said agreeing to a potential delay was playing into an EU attempt to drag the UK “into deep waters”. Raab said: “George Eustice referred to frankly the dishonourable way that they have tried to bully us and shove us around and it is time for us to stand up and show some mettle.

“It is very clear that they [the EU] have used … Northern Ireland with all the sensitivities around that, in order, effectively, to try to lock us into a range of their laws, really just to undercut our competitive advantage … Trying to use Northern Ireland, given the history of that conflict, given the secessionist tendencies in other European countries, in order to put pressure on us in the way that they have, I don’t think that’s right.”