Boris Johnson’s Brexit plan is impossible as the UK will not be able to leave the EU with a deal or without a deal by the end of October, Philip Hammond, the chancellor, has said.

Hammond, who is fighting against no deal, cast doubt on the viability of the Brexit promises of Johnson and other Tory leader contenders such as Dominic Raab as he gave a speech in Westminster.

He said many of the candidates were pledging things that they could not deliver during their campaigns which they may have to go back on later.

Asked whether Johnson’s plan to leave on 31 October would work, he said: “I don’t think so … I think it’s not sensible for candidates to box themselves into a corner on this. Parliament will not allow a no-deal exit from the EU and our experience has suggested it may not be that easy to secure a deal in parliament.”

The idea of leaving with a deal by that date would be “very difficult or impossible”, he said.

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Johnson has promised to overhaul Theresa May’s withdrawal agreement negotiated with the EU and then get it through parliament by the end of October.

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Hammond, speaking at a Bloomberg event, said: “Boris and any others are perfectly entitled to say that they need to go and test that for themselves but I can advise them that the EU is not likely to be prepared to reopen the withdrawal agreement that we’ve already negotiated with them.”

He highlighted parliament’s opposition to leaving the EU without a deal as a cross-party group of MPs mounted their latest efforts to legislate against that outcome.

Hammond said: “Parliament will no doubt be very interested to hear what the new prime minister has to say but in my mind parliament is not going to change its decision that it will not license a no-deal exit.

“So I think it will be very difficult, in fact I think it will be impossible to do this by 31 October and I don’t think it will be in our national interest to drive toward this cliff edge.”

The chancellor warned the candidates against making an array of unfunded spending commitments, such as Johnson’s pledge of sweeping tax cuts for higher earners.

“Be mindful of the fact that so long as no deal is a risk,” he said. “We need to retain a war chest to protect our economy from the immediate shock of a no-deal Brexit ... Until no deal is definitely off the table, we need to retain that firepower.

“I would caution any leadership contenders in going beyond committing the headroom we know we already have and starting to move into the realms of unfunded spending or tax cutting commitments. It is simply not the case, as some people have asserted, that tax cuts pay for themselves.”