The risk to peace in Northern Ireland from Brexit was exaggerated and was used by opponents “to trap the UK in the EU”, Boris Johnson has claimed in his memoir.

The former prime minister’s new book, Unleashed, reveals that many family members urged him to back remain, and concedes that the true figure for UK weekly contributions to Brussels were about half the £350m famously put on the Vote Leave bus.

Settling scores with a number of Conservative former colleagues, he calls David Cameron’s departure as PM immediately after the Brexit vote a “flouncerama” and sets out his sadness and anger at Michael Gove for standing against him to be Tory leader in 2016.

While large sections of the 733-page book deal with Johnson’s time as London mayor, it covers the Brexit period in detail, including the deadlock between 2016 and his election victory in 2019, something he blames in part on worries about a resurgence in IRA violence in Northern Ireland if border arrangements changed.

In the months after the Brexit vote, “the establishment in Britain combined with the EU to try and make a nonsense of Brexit and make it impossible to deliver”, he writes.

Discussing talks with the EU and European leaders over a planned withdrawal agreement in August 2019, shortly after he took over in No 10, Johnson claims they used Northern Ireland as an excuse to hold things up further.

“They wanted to rope-a-dope us, to see how long I could last,” he writes. “They were in an immensely strong position and they knew it.

“They had managed electrically to cross-wire the ambition of Brexit with the cause of peace in Northern Ireland, and anyone who disagreed with them – anyone who wanted to take the whole of the UK out of the EU – was at risk of being electrocuted, pssssscht, on a charge (however exaggerated) of putting that Northern Irish peace at risk.”

The book goes on: “It was that fear – let us be blunt, the fear of renewed IRA activity – that was being used to trap the UK in the EU. The argument was that once the UK had left, there would be a new land border with the EU, along the border between Northern Ireland and the Republic.”

In another section of the book, about the buildup to the EU referendum, Johnson reveals that before he publicly supported leave, his father and all his siblings urged him to back remain, although his then wife, Marina Wheeler, was “inclining towards leave”.

The same chapter confirms that Johnson wrote two versions of a Telegraph article in which he was to declare his decision, one in favour of Brexit and one against. It says the latter, however, was “a really hasty and half-baked pastiche of a column” intended to make sure he did support leave.

Describing the referendum campaign, Johnson accepts that the claimed £350m-a-week outlay was in fact nearer £175m when treated as a net amount, while adding: “That was still a hell of a lot of money.”

He nonetheless defends the tactic: “It was a brilliant slogan because it had what they call cut-through. It became the subject of discussion up and down the country, and it was the remain campaign that did the work for us – by massively intensifying the impact of what we were saying.”

The remain campaign, in endlessly criticising the slogan, “made the cardinal mistake, in any campaign, of playing on our turf”, he writes.

Immediately after the referendum, Cameron announced he was resigning as prime minister, something Johnson criticises heavily. Describing Cameron’s departure statement in Downing Street, he writes: “He was walking back inside the black door and whistling some jaunty air, as though to say to us, the victors – right, you tossers, you’ve made this mess. Now you sort it out.

“I thought it was the wrong thing to do, and a bit petulant. Plenty of other European leaders sustain referendum defeats and carry on with their duties.”

In another settled score, Johnson condemns Gove for initially backing him to succeed Cameron before announcing his own shock candidacy, a move that led Johnson to pull out of the contest.

“To this day I don’t know exactly why he did me in. He had all sorts of voices in his ear. George Osborne was certainly urging him to run,” Johnson writes. “I particularly disapproved of the way he started slating me publicly in order to justify his own decision. What I resented most was the sheer stupidity of what he had done.”