Senior figures in Change UK have expressed concern that the People’s Vote campaign may fall foul of electoral law, accusing key staff at the non-partisan campaign of taking orders from Labour.

Among those who have made complaints are the Change UK MPs Chuka Umunna, formerly of Labour, and Anna Soubry, a former Tory, both founding members of the campaign.

The Guardian understands that other parties, including the Lib Dems, have also expressed concerns about how the campaign has portrayed Labour’s position on a second referendum.

Senior figures in the People’s Vote campaign include Alastair Campbell and Tom Baldwin, Ed Miliband’s former spokesman.

The allegation has been fiercely disputed by the People’s Vote campaign, which said it had repeatedly criticised Labour’s position on Brexit for being too weak. It denied that the party had had undue influence in its campaign.

The row spilled into the open last week after senior People’s Vote staffers were accused of persuading a pro-remain activist, Femi Oluwole, to drop his independent candidacy in the Peterborough byelection, where he would have been backed by Change UK, the Lib Dems and the Green party. A Change UK source said the candidate was “subject to the most extreme pressure by Labour figures in the People’s Vote campaign”.

“The members of staff of the PV campaign are supposed to be independent, non-partisan and cross-party,” the source said. There’s a legal obligation on them to be so because otherwise under electoral law their spending could be deemed to be part of the Labour party’s spending.”

Senior sources close to the discussions alleged that People’s Vote staffers threatened to expel Oluwole’s grassroots campaign Our Future, Our Choice (OFOC) from the People’s Vote coalition of organisations.

That allegation was robustly denied by sources in the People’s Vote campaign, who claimed Oluwole was merely warned that OFOC would not be able to be part of a non-partisan campaign if he stood for election and that it could fall foul of data protection rules if he attempted to use supporters’ data for his election.

Change UK sources said a number of complaints had been made about the perceived reluctance of the People’s Vote campaign to criticise Labour’s position on Brexit. “There are big questions over its impartiality,” one Change UK source said. “A number of parties now have complained about the extent of that Labour influence.”

Another issue that has raised the hackles of pro-remain parties including Change UK and the Lib Dems is the “People’s Vote test” on the campaign’s website, which gives Labour a tick for supporting a referendum.

“Who in all seriousness would do that, given what their manifesto says?” the Change UK source said. “In all credibility, you could not describe the Labour party as a People’s Vote party … but the People’s Vote campaign persist in doing this – at the behest of the Labour-orientated people running the organisation. It’s becoming a real problem.”

Oluwole has said it was his decision alone not to stand in Peterborough. “There was a very real possibility that my taking part in that byelection would take votes from Labour and help Nigel Farage, via his Brexit party candidate,” he said. “Second, my gut was screaming: Femi, you’re not from Peterborough. The people of Peterborough deserve an MP who knows them and their city.”

A People’s Vote spokesperson said: “The People’s Vote campaign is not and never will be a political party. We are navigating the European parliamentary election as a cross-party campaign and, of course, we won’t always do everything in a way that pleases everyone.”

The spokesman said the website, campaign literature and press releases described Labour’s policy as “mealy-mouthed” and “lukewarm”, but the party had “done the bare minimum needed to scrape a pass on a People’s Vote test because it backs giving the public the final say on the government’s Brexit deal – which is the only one currently on the table.”