In light of Boris Johnson delaying his own interview with Andrew Neil and possibly refusing altogether, John McDonnell has warned the BBC that it needs to "wake up" as it is "being played" by the Prime Minister.
The BBC said its first priority "must be its audience".
Conservatives Boris Johnson has cancelled his campaigning while he deals with the fallout from the London Bridge terror attack.
Mr Johnson offered to appear on Mr Marr's programme, but the broadcaster turned him down because he would not submit himself to examination by Mr Neil, The Daily Telegraph reported.
The corporation's decision to schedule the interview with Marr has been criticised by Labour.
He won't be doing Marr until we have confirmed and announced a date for the Neil interview.
Former culture secretary Ben Bradshaw tweeted that it was a "shameful and abject surrender" by BBC management.
In a tweet, Ilford North candidate Wes Streeting said: 'I love the BBC and hate the regular attacks on its impartiality and the professionalism of its journalists, particularly when it has some of the very best in the business.
Labour had accused Johnson of avoiding Neil, insisting it had agreed to let Jeremy Corbyn appear on the programme in the belief that the prime minister was already signed up. But this decision is wrong.
He said: 'The reason he is doing it is because he thinks like, you know, his Bullingdon Club friends, that they're above the rest of us.
Tory bosses have said they are "in discussions" with the BBC, but no agreement has been reached.
Mr Johnson snubbed a Channel 4 debate on climate change last night as the broadcaster replaced him on stage with an ice sculpture.
The BBC's interview with Lib Dem leader Jo Swinson is set to air on 4 December.
During the debate, from 7pm-9pm, each representative will have one minute for their opening statement and 45sec for a closing statement.