A cross-party amendment to push for a second EU referendum will not be tabled in the Commons as it would have little chance of being passed without formal support from Labour, the MPs organising it have announced.

Sarah Wollaston, the Conservative MP who has led efforts on a so-called “people’s vote” amendment, said that without the backing of Jeremy Corbyn, “at the moment we would not have the numbers”.

However, the Liberal Democrats have tabled a similar amendment and have called for Labour to back the idea.

Speaking outside parliament alongside the Labour MPs Luciana Berger and Chuka Umunna, Wollaston urged Corbyn to think again. “We would like to appeal again to him to give his unequivocal backing to a people’s vote, in which case we could make progress,” she said.

Labour has not ruled out supporting a second referendum and the party is keeping its options open. There is disquiet among some of its MPs and shadow ministers that backing such an option could anger leave-backing Labour voters.

Wollaston argued that a second referendum was still the best option to end the Brexit deadlock. “People have a right to change their minds, and the mandate from the first referendum – over two years ago and based on entirely unrealistic promises and outright lies – has expired.”

But without Labour backing, she said, “that amendment could not pass, and so with great regret we will not be laying that amendment”.

Berger said that with 30 scheduled Commons sittings left before the current Brexit date, there was “an urgent need for leadership”.

“Regrettably, the Labour leadership won’t commit to an achievable policy,” she said. “And yet we know that the majority of Labour voters, supporters and members want a final say on any Brexit deal. At a time when Labour should be championing a people’s vote, the leadership avoids answering that call.”

More than a dozen amendments have been tabled so far to be potentially voted on next Tuesday, covering areas including extending article 50, holding non-binding, indicative votes in the Commons on the way forward, and dictating an end date for the Irish backstop.

Among these is one signed by all of the Liberal Democrat MPs to back a second referendum. The party’s Brexit spokesman, Tom Brake, said: “There is still time to act in the national interest. Jeremy Corbyn and the Labour leadership must stop dreaming up more and more creative excuses for refusing to support a people’s vote, which their members and supporters want.”

Not all the amendments will be selected for a vote. The choice will be made by the Commons Speaker, John Bercow.

They are officially amendments to the statement made to the Commons by Theresa May on Monday following the overwhelming defeat of the PM’s Brexit plan. Such a statement, officially titled a motion in neutral terms, cannot normally be amended. However, the procedures of the house were changed after an earlier amendment by the Tory MP Dominic Grieve.