A coalition of MPs and others have launched a campaign to hold pro-Brexit politicians to account for promises made during the referendum campaign.

Vote Leave Watch, an unofficial spinoff from the remain campaign, is being led by Labour’s Chuka Umunna, who said the aim was to highlight the actions of pro-leave politicians who might seek to “wriggle out of the promises that they made to the electorate”.

Norman Lamb, the Liberal Democrat MP, Richard Reed, a co-founder of Innocent Drinks, and the TV presenter June Sarpong, all of whom were involved in the Britain Stronger in Europe campaign, are supporting the movement.

Umunna said the hope was to expand the organisation and to solicit wider research on both the detail of claims made by specific Brexit-backing politicians and whether these were being breached.

He said it was not just on behalf of the 48% of people who voted to remain in the EU. “They [Brexiters] made very clear, often overblown claims to the electorate,” Umunna said. “In a democracy it’s very important that they’re held to account for that. I think that would be a big concern to the 52% as well. They will want to know whether the things they were promised will be delivered.”

Umunna added: “If anger was in part driving some people to vote for us to leave the European Union, if they now find that all the things they were promised would happen in the event that we leave don’t happen, and they find themselves in a worse situation, they’re going to have an expectation that somebody’s held to account for that.”

The leave campaign attracted criticism for a series of its headline claims before the referendum, notably that Brexit would save the UK £350m a week to spend on the NHS, and that withdrawal from the EU would have no adverse effect on the economy.

Leading leave figures including Michael Gove and Iain Duncan Smith have already backtracked on the NHS claim, while the value of sterling has tumbled and there has been turmoil in commercial property and other sectors.

Reed said it was “vital for the health of democracy” that politicians were held accountable for promises over such an important issue. He said: “Whether you voted in or out, we all have a shared interest in making sure the commitments made by Vote Leave are adhered to.”

Umunna, a former shadow business secretary who stepped down from the Labour frontbench shortly after Jeremy Corbyn became leader, conceded that more of this work could be done by his colleagues.

“The Labour party should be doing this right now and isn’t because of the issues we have in the party,” he said.

But he argued that with the next government likely to be dominated by Brexit proponents regardless of who wins the Tory leadership contest, a broader approach was needed. “We will make sure that everything they said will happen is put to them on a regular basis,” he said.