Labour and the grassroots campaign group Momentum are putting their activists on notice for a snap general election after Boris Johnson’s first full day as prime minister, though some of the party’s MPs have said it must adopt a clear remain position in any pre-Brexit manifesto.

Jeremy Corbyn launched five election pledges at a rally on Thursday night, including a public vote on any Conservative Brexit deal, in which Labour would campaign to remain – but crucially only “against no-deal or a bad Tory deal.”

Other pledges included increased funding for the NHS, a living wage of £10 an hour, a job-creating green industrial revolution, and free school meals for primary school children.

Some MPs believe there is still a lack of clarity over what the party’s Brexit position would be in a forthcoming election. The party has not spelled out what its position would be in a future snap election manifesto, if Labour were able to attempt to renegotiate a Brexit deal themselves.

The shadow Treasury minister Clive Lewis, a key ally of Corbyn, said it was time the party made it clear it would fight a snap election on a remain platform.

“We have rightly been demanding a general election for months, and we are probably about to get one. We need to grasp this moment as a huge opportunity,” said Lewis, a member of the Love Socialism Hate Brexit group of pro-referendum leftwing MPs.

“Boris is dangerous, but he can be roundly defeated by the popular, radical programme that only Labour can deliver. But to stand any hope at all either of winning or of being able to deliver on our promises, we need to be an unequivocal party of remain.

“This isn’t just a matter of electoral calculation – for our members, as for many of our voters, Brexit is bound up with an agenda of deregulation and racist scapegoating. Boris Johnson illustrates that, and we in Labour need to connect the dots.”

Labour’s Peter Kyle, one of the MPs behind moves in parliament to attach a referendum to any Brexit deal, said: “If a general election is imminent, you can’t have one government deal that claims to represent the will of the people, then have a new prime minister with a new deal and still believe it, too, represents the will of the people in 2016.

“Labour has accepted the need for a confirmatory public ballot, its MPs have voted for it overwhelmingly, its members support it and so does its leader. It’s time to say we will back remain in any future referendum, so we speak with more clarity, more conviction, and solve this crisis once and for all.”

At the dispatch box in the Commons on Thursday, Corbyn said the new prime minister should “go back to the people” with any new Brexit plan and said his party would oppose a Brexit deal that failed to protect jobs, workers’ rights and environmental protections.

“If he has the confidence to put that decision back to the people, we would campaign to remain,” he said.

Corbyn told the rally in Westminster that Johnson was unelected by the majority of the country and framed the choice as a straight one between Labour or Johnson’s hard-right cabinet. “You deserve your say. Whether that’s in a public vote on Brexit or in a general election, so everyone has the chance to decide the future of our country,” he said.

“The choice will be between Johnson’s divisive government for the wealthy few – and a radical Labour government that will bring the country together and deliver for the many.”

Labour alsoemailed supporters on Thursday seeking donations to fight a snap poll, drawing attention to the number of advertisements the Conservatives had bought on social media after Johnson’s win in the Tory leadership contest.

“Boris Johnson knows it: there’s a general election brewing, and he’s spending big to win it,” the email said.

“Just last night, the Tories flooded Facebook with 554 political adverts, with hard-right Vote Leave political strategist Dominic Cummings masterminding the move. It’s scary stuff. We have to fight back, and it’s our members that will help do it.”

Momentum said it had ramped up preparations for an imminent poll. It has plans to mobilise tens of thousands of Labour members, building a viral video response unit to make targeted social media videos for marginal constituencies and embarking on a fundraising drive to raise hundreds of thousands of pounds.

The group said it was updating its “my nearest marginal” platform, which sent thousands of campaigners to targeted constituencies at the 2017 election, and expanding its programme to train thousands of members to have persuasive conversations on the doorstep.

Laura Parker, Momentum’s national coordinator, said: “During the 2017 snap election we operated on a tiny budget, punched well above our weight and mobilised thousands of activists to swing key seats for Labour. This time we’re going bigger: using new organising techniques from the Bernie Sanders campaign to build a general election campaign the likes of which Britain has never seen.”

Labour’s preparations for a general election could be hampered by turmoil in the party after MPs were told local parties could begin using trigger ballots, which can force sitting MPs to run against other potential candidates for their seats.

A number of Labour MPs, including Kate Hoey, Jim Fitzpatrick and Gloria De Piero, have said they will not stand again at the next election.