Labour will not allow a representative of the People’s Vote campaign to take part in any televised Brexit debate involving Theresa May and Jeremy Corbyn, with the party instead pushing for a format that would allow the opposition leader to criticise the prime minister’s domestic policies.

May’s team has proposed holding a live primetime TV debate ahead of a crunch parliamentary vote next month on Britain’s exit from the EU, prompting a discussion over the debate format and which broadcaster would host it.

It also led to calls from parties that support a second EU referendum – including the Scottish National party, the Green party and the Liberal Democrats – to have a representative on the panel.

Corbyn’s team swiftly jumped at the offer and confirmed their willingness to take part, saying: “Jeremy would relish a head-to-head debate with Theresa May about her botched Brexit deal and the future of our country.”

Despite this, there is no certainty that Corbyn will be involved if Labour cannot agree terms with a broadcaster and No 10 in the next fortnight.

Sources aware of Labour’s plans emphasised the party would only be willing to consider a debate that pitched the two main party leaders against each other, leaving no space for an proponent of a second referendum. Labour believes this format would also allow Corbyn to get May to broaden the debate beyond Brexit and hold her to account on issues such as austerity.

Anti-Brexit groups called on broadcasters to insist on including a supporter of a second referendum.

“While it is welcome that the prime minister is finally agreeing to turn up to a debate, the argument for the people to be given the final say on Brexit must be heard loud and clear in that discussion,” said the Best for Britain chief executive, Eloise Todd.

One Downing Street source said formal talks with broadcasters had yet to begin, with questions around scheduling still to be decided. The BBC is the most likely home for a debate, but Sky News, Channel 4 and Channel 5 are among those who are thought to have expressed an interest in giving a platform to the prime minister.

Discussion about the format of leaders’ debates has become a cornerstone of British politics over the past decade, with months spent trying to agree a debate format during the 2015 general election. Time pressure means political parties have a matter of days to come to an arrangement this time.

The Daily Telegraph has been briefed that the prime minister favours holding a “primetime, Sunday night televised debate” with Corbyn, with a “Question Time-style session with a televised audience hosted by David Dimbleby” lined up if terms cannot be agreed with the Labour leader.

However, Downing Street’s desire for a peak slot may come against the brutal reality of TV schedules. The prime minister’s team want the largest possible audience for such a debate, but the only logistically possible Sunday night that could work is 9 December, which could bring its own problems if they wish to appear on one of the biggest terrestrial channels.

That evening, BBC One is set to show Countryfile, the season finales of Doctor Who and David Attenborough’s Dynasties, plus Strictly Come Dancing and a new drama by Jimmy McGovern. Meanwhile, ITV will be showing the final of I’m a Celebrity … Get Me Out of Here.

It is unlikely that a sceptical audience settling down for Sunday night viewing would welcome any of the shows being interrupted or delayed, even for a political debate that could shape the future of Britain.

Any leadership debate will also inevitably provide comparisons with the 2017 general election debates, where May declined to take part and instead sent Amber Rudd to deputise against Corbyn.

During a Facebook Q&A last year, she justified skipping the head-to-head contest with her Labour rival: “What I think is more important is actually that I and he take questions directly from the voters”