The chancellor, Philip Hammond, has urged hard Brexiters to vote for Theresa May’s withdrawal deal or risk a soft Brexit compromise, even if concessions on the backstop can’t be secured from the EU.

Hammond admitted that convincing Brussels to accept legal binding changes to the backstop on the Irish border was proving a “challenge”.

Speaking to BBC Radio 4’s Today programme, he said that even if those assurances could not be secured, he urged the “Brexit wing of the party” to get behind the deal in the crucial meaningful vote next Tuesday or risk uncertainty over Brexit.

His warning came after France urged the UK negotiating team, headed by the attorney general, Geoffrey Cox, and the Brexit secretary, Stephen Barclay, to come up with fresh proposals to end the Brexit impasse.

Hammond said: “I hope they [Cox and Barclay] will come back with an offer that my colleagues on the Brexit wing of the party will consider very, very carefully in the context of the real situation that we are in, because if the prime minister’s deal does not get approved on Tuesday then it is likely that the House of Commons will vote to extend the article 50 procedure to not leave the EU without a deal, and where we go thereafter is highly uncertain.”

He added: “For those people who are passionate about ensuring that we leave the EU on time, it surely must be something that they need to think very carefully about now, because they run the risk of us moving away from their preferred course of action if we don’t get this deal through on Tuesday.”

The chancellor said failing to back the deal could involve signing up to a customs union compromise currently being discussed by senior Tory backbenchers and Labour’s leadership.

Hammond said: “The Labour party has been talking for a long time about the idea of a customs union grafted onto the PM’s deal. Those of my colleagues who feel very strongly against that proposal need to think very hard about the implications of voting against the prime minister’s deal next Tuesday, because we will then be in unknown territory where a consensus will have to be forged across the House of Commons and that will inevitably mean compromises being made.”

He also pointedly refused to say whether he would resign from the government if the prime minister instructed MPs to vote for a no-deal Brexit on Wednesday if her deal was rejected on Tuesday.

He said: “I’ve always said that I believe that it would be a very bad outcome for the UK to leave the European Union without a deal, but there isn’t a motion yet … so I can’t say how I will vote on a motion that hasn’t been tabled.”

Hammond suggested that the government would not whip MPs to vote for no deal.

He said: “I think the government is very clear where the will of parliament is on this. Parliament will vote not to leave the EU without a deal next Wednesday. I have a high degree of confidence about that. But we do need to have a clear confirmation.”

Hammond also claimed that more money would be available for public spending if MPs voted for May’s deal.

He said: “We have got a spending review coming up this summer that will set budgets for the next three years. We will have more money to spend on public services and, if we get the right Brexit deal done and a smooth exit from the European Union so that we can release the money that we have set aside to deal with the possible disruption of a no-deal exit, then that will give us more money still.

“If the money is spent on dealing with the disruption of a no-deal exit it can’t be spent on policing, on social care, on schools, on higher education, on defence and all the other things that people are expecting.”