Boris Johnson will be interviewed on the BBC’s Andrew Marr Show on Sunday, the broadcaster said, going back on a pledge to refuse the prime minister a platform unless he agreed to an on-air grilling with Andrew Neil.

The broadcaster said it was necessary to provide a slot for the prime minister in the wake of the terror attack on London Bridge that left two people dead and three injured after convicted and released terrorist Usman Khan stabbed members of the public.

In a statement, the corporation said: “As the national public service broadcaster, the BBC’s first priority must be its audience. In the wake of a major terrorist incident, we believe it is now in the public interest that the prime minister should be interviewed on our flagship Sunday political programme.

“All parties’ election policy proposals must – and will – face detailed scrutiny from us and we continue to urge Boris Johnson to take part in the prime-time Andrew Neil interview as other leaders have done.”

It follows tough interviews by Mr Neil with Labour’s Jeremy Corbyn and the SNP’s Nicola Sturgeon, with both saying they had agreed to the interview on the understanding the Conservative leader would follow suit.

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Labour’s Ben Bradshaw, a former culture secretary, said: “This is a shameful and abject surrender by the BBC management, which will leave professional BBC journalists absolutely horrified and in despair with an organisation where morale is already at rock bottom.”

The party’s Wes Streeting added: “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. But this decision is wrong. The BBC have been played by the Tory leader and shouldn’t dance to his tune.”

It comes after shadow chancellor John McDonnell said the BBC is being “played” by Mr Johnson over the interview.

Reacting furiously over the organisation’s admission they are “not yet able to fix a date”, shadow chancellor John McDonnell said the Conservative leader was pushing the interview date beyond the postal vote returns.

“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.”

He continued: “That they don’t need to be held to account. They don’t need to be treated like the rest of us. And so what he’s doing now is he’s avoiding, he’s running scared.