MPs are expected to launch a fresh attempt to block a future prime minister pushing a no-deal Brexit policy by threatening to cut off vital funds for government departments.

The cross-party plan, led by Conservative MP Dominic Grieve and senior Labour MP Dame Margaret Beckett, aims to force the future Tory leader to gain parliament's consent for leaving the EU without a deal.

Their amendment to routine finance legislation in the Commons – referred to as "estimates" – would cut off funding for government ministries if the PM failed to do so.

Boris Johnson, the frontrunner in the race to replace Theresa May as Conservative leader, said this week the UK will leave the EU on 31 October "do or die" - heightening the risk of a no-deal scenario.

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At the latest Conservative hustings, the ex-foreign secretary again refused to rule out suspending parliament to leave the EU without the consent of the Commons, but claimed the odds of a no-deal Brexit were a "million-to-one against".

But Mr Grieve, the former attorney general, told The Sun: "The suggestion that we could or should be taken out of the EU without the consent of the House of commons is fundamentally wrong, and frankly unconstitutional.

"The fact that it is being suggested as a viable option is unacceptable. The Commons should put down such markers as it can that such a course of action is unacceptable."

The action would be a step down from the "nuclear option" of Conservative MPs voting against their own government in a no confidence motion to prevent a no-deal Brexit, but would have serious ramifications for the future prime minister.

It would deprive funds to critical Whitehall departments to pay for key public services such as schools, welfare, and international aid, The Times added.

The Liberal Democrats said on Wednesday evening they would back the plan, and the party's Brexit spokesperson, Tom Brake, said: "With [Mr] Johnson issuing blood-curdling cries that he will inflict a no deal on the UK, regardless of whether it is opposed by a majority of MPs, rational MPs must use every opportunity to block his reckless impulses."

But Downing Street condemned the move, as a No 10 spokesperson told journalists: "We don't know if that amendment is going to be selected at this point. Any attempt to deny vital funding to Whitehall departments would be grossly irresponsible.

"This is government spending for this financial year and funds crucial areas like schools, housing and welfare."