Jeremy Corbyn has said that he wants Theresa May to debate with him in a one-on-one format, amid a continuing dispute over which broadcaster would host the event and in what format it would be held.

The main broadcasters have proposed their own respective formats after Labour accepted a challenge from the prime minister to debate with Corbyn about her Brexit deal on live television.

The BBC’s would include a panel of 20 prominent commentators that are equally split between supporting and opposing May’s Brexit deal, while Sky and ITV’s bid would be a more straightforward head-to-head.

Labour has claimed the BBC format would be “messy and confusing”, and presents May with the opportunity to cast her opponents as divided since one side would be unanimous in its support for her plan.

“Theresa May said she wanted a head-to-head debate with me on her botched Brexit deal and I am ready to do that,” tweeted the Labour leader. “ITV have a straightforward plan. If she and her team prefer BBC, she should join me in asking them to arrange an actual head-to-head debate.”

His comments followed an increasingly bitter row over whether the BBC had discussed a May-Corbyn debate with Downing Street before Sunday, when the Telegraph reported that the prime minister had challenged the Labour leader.

The broadcaster then appeared to encourage Corbyn to accept its format in a tweet that said May had accepted the offer. “We’re delighted she’s agreed and hope to hear soon from the Labour party,” the BBC press team wrote on Thursday.

Like everyone else, we've just heard the Prime Minister has accepted the BBC’s offer to take part in a debate on the Brexit deal on Sunday 9 December. We’re delighted she’s agreed and hope to hear soon from the Labour party. (1/2) — BBC News Press Team (@BBCNewsPR) November 29, 2018

The row was said to have highlighted the influence of May’s communications chief, Robbie Gibb, who until last year was the BBC’s head of political programming and was responsible for organising the corporation’s election debates.

Labour-supporting campaigners also pointed to other high-profile appointments made by senior Tory ministers from the BBC as evidence that the corporation is currently biased towards the government.

“The ball is in Labour’s court,” said a Downing Street source on Saturday.

May has said she will only take part in a debate against Corbyn, not any hard Brexiter, such as Boris Johnson, or any campaigner for a second referendum, saying the country had moved on from the leave versus remain argument.

She said her TV debate with the Labour leader would not be about the same arguments as the 2016 referendum, during which there were multiple live debates from all factions. Anti-Brexit campaigners have argued that excluding smaller parties from the debate is undemocratic.

On Saturday evening the BBC said: “Our proposal is to broadcast a programme which includes both a head-to-head debate between the prime minister and the leader of the opposition and also an opportunity to hear from a wider range of voices.

“After all, a broad range of views on this issue is held by the public and by parliamentarians – from those who want a different form of Brexit to those who want another public vote – and we believe that should be reflected in the debate.”