David Cameron and Boris Johnson wrestled like “immature schoolboys” over briefing papers in cabinet last summer in an incident described by Channel 4 political correspondent Michael Crick as “hugely undignified, yet hugely symbolic” of the pair’s competitive relationship.

Writing in the Radio Times about the parallel lives and growing rivalry between the prime minister and former mayor of London, Crick said Cameron told journalists the revealing anecdote at a Westminster garden party last year.

He wrote: “Earlier that week, Cameron explained, the pair had sat facing each other in the cabinet room, with Johnson outlining his plans for London and requests for help.

“Then, as Cameron started responding, with help from a sheaf of briefing papers, Johnson leant across the table. ‘What’s all this? Let’s see!’ he cried as he tried to snatch the documents from the PM’s grasp.

“Cameron held on to his precious notes, and for a few moments the two Conservative politicians wrestled and tugged for supremacy across the cabinet table, like a couple of immature schoolboys. Officials looked on in astonishment. It was hugely undignified, yet hugely symbolic.”

Both Cameron and Boris attended Eton and were members of the Bullingdon club at Oxford. However, while Johnson initially backed Cameron in his bid to become party leader, he has quickly become seen as one of the main rivals to Cameron’s leadership of the Conservative party.

Johnson’s backing for the campaign to leave the EU has brought the rivalry more firmly into the public eye, with Crick repeating suspicions among many, including former conservative minister Ken Clarke, that Johnson’s support of Brexit is “a deliberate ploy both to destabilise Cameron, and reinforce his position as darling of the grassroots when the PM calls it a day”.

Crick had a run-in with Johnson while broadcasting from a Vote Leave rally last month when Johnson told supporters to interrupt a Channel 4 broadcast in scenes reminiscent of the hostile attitude towards the media at Donald Trump rallies.

Though one of the attendees approached Crick and asked him to stop recording while placing himself in front of the camera, the Channel 4 reporter later defended Johnson on social media, saying it was unfair to compare him to the controversial presidential candidate and that Johnson was a “very media-friendly politician”.