David Cameron offered Boris Johnson a senior cabinet position in return for campaigning for the UK to remain in the EU during the 2016 referendum, it has been revealed

In the event, and with four months to go before the vote, Johnson transformed the terms of the debate by announcing in February 2016 that “after a huge amount of heartache” he was throwing his weight behind the campaign to take Britain out of the EU.

Lord Cameron told a BBC documentary to mark the 10th anniversary of Brexit that he had offered Johnson – a sometime friend and long-term rival in the Conservative party – a “top five” position, such as defence secretary, on the condition that he did not support the push to leave.

In the programme, Johnson speaks of being invited in early 2016 by Cameron, who was then the prime minister, to play tennis and discuss his position on the forthcoming poll.

“He then said: ‘Look, would you consider joining us on the remain campaign? It’d be much better if … I’d love to have you in the cabinet. You should have a top five job,’” Johnson says. “And I wasn’t sure what the exact hierarchy was. I obviously thought about it out of pure curiosity – what was this job? There’s prime minister, chancellor, home secretary, foreign secretary. That’s four. What is the fifth? A mystery.”

The revelation is made in the first episode of a two-part BBC documentary on the referendum, A Very British Civil War, which will be broadcast on 8 June.

Cameron told the documentary: “I didn’t say which job it was, I said: ‘Be in no doubt, defence is a top five job, for instance.’ I wanted him to understand that I valued his contribution, that he would be a major part of the government going forward.”

The tennis match took place at the US ambassador’s tennis court next to Regent’s Park, which Cameron said he could use in a “wonderful deal” as a place to go for rest and recreation.

Craig Oliver, who was Cameron’s director of communications at the time, said the then prime minister returned from the tennis match “feeling doubly good”. “One, that he’d beaten Boris Johnson at tennis, and two, that he may have a concession that he would actually join the government,” he said.

Johnson’s move to back Brexit was ultimately a blow to Cameron, who pleaded with him earlier on the day his decision was announced to avoid “linking arms” with Nigel Farage and George Galloway in backing a British exit from the EU.

Michael Gove, the justice secretary and Johnson’s close cabinet colleague at the time, had already announced that he too would be campaigning to leave.