Both BBC and ITV are pushing ahead with plans to host a Sunday evening televised Brexit debate between Theresa May and Jeremy Corbyn, despite the physical impossibility of the prime minister and the Labour leader being in two different television studios at the same time.

The farcical situation has occurred because neither political party is willing to back down on its preferred debate format. As a result both broadcasters are now officially insisting they are continuing with preparations for their own rival debates in five days’ time, with no idea which leaders – if any – will turn up to their event.

However, there is the possibility of a breakthrough on Tuesday as negotiations continue.

Discussions began last week, when Theresa May issued a challenge to the Labour leader, urging him to come on national television and debate her Brexit deal with the European Union – an offer that Corbyn’s team immediately accepted. Rival broadcasters then began bidding against each for the right to host the programme on their channel, with proposals for slightly different formats.

ITV suggested a simple head-to-head format on Sunday evening, hosted by Julie Etchingham and with no studio audience. Labour swiftly let it be known that they preferred this format and were ready to sign up with the commercial broadcaster, because it will maximise the amount of direct discussion between the two party leaders.

The BBC proposed a different format, featuring opening statements from both leaders but also including a panel of experts and representatives of smaller political parties who both support and oppose Theresa May’s Brexit deal. Downing Street strongly prefers this option and insist this is the only debate that they are willing to take part in.

As a result both political parties are now claiming that they have fulfilled the terms of the original challenge and it is up to the rival party to blink first and accept the other’s favoured debate format.

The broadcasters are also standing firm and pushing ahead with preparations.

“ITV have invited the prime minister and leader of the opposition to appear in an ITV programme this Sunday evening,” the commercial broadcaster said in a statement on Monday night. “Invitations remain open. As always, it is up to those invited to decide whether they want to accept the invitation.”

The BBC, in its most recent comment on the issue, defended its proposed format: “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.”

It is unclear whether either broadcaster would be willing to publicly empty-chair either May or Corbyn if they fail to turn up, given the highly unusual situation.

On Saturday David Cameron’s former director of communications Craig Oliver, who was involved in organising the 2015 general election debates, suggested the debate over the debate was “displacement activity” which distracted from the real issue of the looming parliamentary vote on the deal.