The Independent Group (TIG) has tabled an amendment in the Commons demanding that the government starts preparing for a second EU referendum, in an attempt to recapture the initiative on Brexit a day after Labour promised to support moves for a public vote next month.

The amendment from the 11-strong group of MPs has the support of the Scottish National party, the Liberal Democrats and Plaid Cymru and is aimed at provoking a fresh split in Labour by wooing MPs who want the party to support a new vote immediately.

Chris Leslie, who defected from Labour last week, called on his former party for support. “If the Labour leadership support this amendment, we could make real progress on a people’s vote. Now is the time to put the national interest first. Parliament must act now.”

In reality, Labour’s leadership is unlikely to support TIG’s amendment because Jeremy Corbyn wants to continue pursuing his own Brexit plan, starting by putting it to a vote in the Commons on Wednesday.

The Labour leader is likely to seek a fresh meeting with Theresa May and will press her to offer civil service support to work his party’s proposals into a coherent plan. Under Labour’s proposals, the UK would remain in a customs union with the EU after Brexit and aim for a close relationship with the single market.

TIG leaders hope that some Labour MPs who have been pressing for a second referendum could yet back their amendment, but one Labour MP who is close to the People’s Vote campaign was sceptical that they would. “Most of us will ignore it, I suspect,” the source said.

In any event, the TIG amendment would have to be selected by John Bercow, the Speaker, to be voted on. It is not certain it will be picked for debate, though the support of Westminster’s third largest party, the SNP, significantly boosts its chances.

If selected it would be the first time that a motion calling for a second referendum has been debated by MPs, but there is no prospect of it passing the Commons because of the lack of Labour backing.

On Monday, Corbyn told a private meeting of his party’s MPs that the Labour leadership would support a second referendum on May’s Brexit deal if Labour could not get a majority behind its own Brexit plan in the coming days.

He repeated the pledge in public, promising that a “confirmatory public vote” would be held if May’s Brexit deal were to pass through parliament next month, despite complaints about the new policy in the shadow cabinet.

Corbyn told MPs: “We cannot risk our country’s industry and people’s livelihoods, so if it somehow passes in some form at a later stage, we believe there must be a confirmatory public vote to see if people feel that that is what they voted for.”

Labour has been careful not to spell out exactly what a “confirmatory public vote” would entail. Corbyn is understood to be believe the party must give leave voters a “credible proposal” that they could vote for in a referendum.

That would not be satisfied by a revised version of May’s deal, even if it had won the support of parliament. But one MP questioned if such a plan made sense. “So, what, we’d back a referendum to oppose our own deal if we managed to get it through parliament?”

Labour sources said there had been a vocal backlash against the decision at a shadow cabinet meeting on Tuesday, with some dissent that it had not been discussed and agreed to at a full meeting of the party body.

John Mann, a backbencher and Brexit supporter, criticised the party’s “absurd” shift to support a second referendum. “Voters won’t have it. The last person to renege on their manifesto was Nick Clegg. It didn’t end very well for him on tuition fees.”

Keir Starmer, Labour’s Brexit spokesman, said he was “well aware of different views across my own party”. Party sources concerned about a second referendum said at least two dozen MPs would vote against or defy the whip in a Commons vote.

Separately, Labour’s deputy leader, Tom Watson, postponed an event for Labour MPs and peers in the party’s “social democratic tradition” that had been due to take place on Tuesday night in Westminster.

It had been billed by some supporters as a chance to rally support in the party against Corbyn’s leadership, but other Labour MPs who might be considered supportive of Watson said any attempt to form a separate grouping to threaten the leader would be unpopular with them.

Friends of Watson said the meeting, open to all backbenchers, would be held in the next couple of weeks instead. “It’ll be a discussion about how to ensure pluralism within the party, how to get the voice of that tradition heard and also positive policy work about future facing issues,” one ally said.