Wrangling over a planned politicians’ TV debate on Brexit due to take place in less than a week’s time has intensified after both Conservative Brexit supporters and the Liberal Democrats formally wrote to broadcasters insisting they should be included.

With Theresa May and Jeremy Corbyn yet to decide between an event on BBC or ITV and trading accusations about the other running scared, a group of Tory Brexiters have sought the inclusion of someone from their side, arguing that the two leaders are too close together on the issue for the debate to be worthwhile.

In a letter to the BBC chair, Sir David Clementi, Boris Johnson, Dominic Raab, Iain Duncan Smith, John Whittingdale, Owen Paterson and Jacob Rees-Mogg said the debate would “breach the concept of impartiality” without the inclusion of a leading Brexiter.

According to the Daily Telegraph, the letter tells Clementi that a debate between the prime minister and Labour leader would “do nothing to illuminate the real issues at stake”, as both supported remain in the 2016 referendum.

“They are both wedded to slightly different models of staying in the customs union,” the letter argues.

Meanwhile, the Liberal Democrat leader, Vince Cable, has written to the heads on BBC, ITV and Sky to argue instead that since May and Corbyn both now back leaving the EU, a debate without him would represent an “egregious imbalance”.

“Such a debate is clearly highly unsatisfactory, and will reveal almost nothing about the alternative options before the country,” Cable wrote. “The principal alternative to the withdrawal agreement is for the UK to remain as a full and influential member of the European Union.

“All the evidence suggests that there is now a majority in the country for doing so, and a substantial majority for a people’s vote. Yet neither Jeremy Corbyn nor Theresa May supports this route.”

As it stands, the plan is for May and Corbyn to line up against each other on BBC1 on Sunday evening, two days before the crunch vote in the Commons on the planned Brexit deal.

However, there is still quibbling between the two sides over the format, and whether it could instead be broadcast on ITV.

A Downing Street spokesman said that in the week since May challenged Corbyn to a debate, “in order to accommodate his confected demands we’ve moved our preferred day, accommodated the addition of social media questions at Labour’s request, and agreed there should be maximum head-to-head time, while still including voices from employers and civil society in the debate”.

The spokesman added: “But if Jeremy Corbyn doesn’t agree to what’s now on the table – a debate on primetime with the prime minister – the public will rightly conclude he’s running scared. So let’s get on with it.”

However, a Labour spokeswoman said May was “running away from the scrutiny of a real head to head debate with Jeremy Corbyn”, as she had in the 2017 election.

“Why else would she not accept ITV’s offer of a straightforward head-to-head debate, as Jeremy has done?” she said. “Instead, her team are playing games and prefer the BBC’s offer, which would provide less debating time and risk a confusing mish-mash for the viewing public.”