The UK could be just days from crashing out of the EU without an agreement before MPs vote again on Theresa May’s deal, a cabinet minister has admitted.

Andrea Leadsom, the Commons leader, twice failed to rule out a delay until after the next EU summit finishing on March 22 – exactly one week before the scheduled departure day.

The prime minister had to abandon hopes for a second ‘meaningful vote’ this week, after the EU rejected her plea for legal changes to the Irish backstop that could win over the Commons.

Asked if that could mean no vote until “the last few days” before the Brexit cliff edge, on 29 March, Ms Leadsom said: “It is a negotiation. It is not possible to predict the future.

“But the meaningful vote will come back to parliament as soon as the issue around the backstop has been sorted out.”

However, Ms Leadsom denied Ms May was planning to inflict a “my deal or no deal” choice, in late March, saying: “No, it’s not running down the clock.”

Instead, she heaped all the blame for “pushing the UK” into the risk of a crash-out Brexit, by failing to compromise on the backstop controversy.

“It would be an extraordinary outcome if the thing the backstop is seeking to avoid – which is a hard border in Northern Ireland – if the EU were so determined to be completely intransigent that they actually incur the very thing they are seeking to avoid,” the Commons leader said.

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The comments come ahead of another statement by the prime minister later today, in which she will urge MPs to give her two more weeks to win over the EU.

On Thursday, a fresh round of Brexit votes will take place, but with little expectation of any amendment passing that will put parliament “in control”.

There is no sign of pro-EU cabinet ministers carrying out their threat to resign unless they are free to vote for moves seeking a delay to the Article 50 process, to avoid a no-deal process.

Without that shift, the amendment put forward by Labour’s Yvette Cooper – to bring forward legislation to force Ms May to seek an extension – is likely to be defeated again.

Labour is expected to seek a second meaningful vote before the end of February, but may lack Tory support to win the vote.

It means the expected showdown is likely to be delayed again, until the next set of votes in just over a fortnight’s time.

Ms May stated publicly that she is not seeking to replace the backstop with “alternative arrangements” – the demand made in the successful Commons vote two weeks ago – although No 10 then tried to backtrack.

Speaking on BBC Radio 4’s Today programme, Ms Leadsom hinted an addendum to the withdrawal agreement – to clarify the impact of, rather than replace the backstop – might be enough.