Jeremy Corbyn has accepted his personal responsibility for Labour’s general election defeat as he gave his fullest explanation to date for the catastrophic losses that helped return Boris Johnson to Downing Street.

Writing in the Observer, the Labour leader, who has announced he will step down when a successor is elected in the spring, describes the results as “desperately disappointing”.

He says he believes Labour paid a price for a Brexit policy that was seen by some voters as an attempt to straddle the divide between remainers and leavers, and by others as wanting to rerun the referendum.

“We have suffered a heavy defeat, and I take my responsibility for it,” he says, in his first note of contrition since Labour seats fell to the Tories across the north of England and the Midlands, giving the Conservatives a majority of 80.

But, as critics tore into his leadership record, for the most part he defends it, blaming a political system that he says has been volatile since the financial crash of 2008, as well as the media and Johnson’s dishonesty, for the result.

Corbyn insists that on many issues Labour had the right answers: “I am proud that on austerity, on corporate power, on inequality and on the climate emergency we have won the arguments and rewritten the terms of political debate.”

I am proud that on austerity, on corporate power, on inequality and on the climate emergency we have rewritten the terms of political debate Jeremy Corbyn

Suggesting that he believes his party would have won and he would have become prime minister if Brexit had not dominated, he adds: “There is no doubt that our policies are popular, from public ownership of rail and key utilities to a massive house-building programme and a pay rise for millions. The question is how can we succeed in future where we didn’t this time?”

As the recriminations continued within the party, and potential successors began laying out their stalls, Corbyn’s closest political ally, the shadow chancellor, John McDonnell, said he would be stepping down from the shadow cabinet.

McDonnell said that while “Jeremy was the right leader”, it was time for the party to move on under new leadership. “We will all go now. The new leader will come in place and appoint a shadow cabinet. I won’t be part of the shadow cabinet. I’ve done my bit. We need to move on at that stage with that new leader,” he told BBC News.

It is understood that Corbyn’s chief supporters will give their backing to McDonnell’s protege, the shadow business secretary Rebecca Long-Bailey, who they hope will carry the torch for the left.

Corbyn says the Tories’ central message – to “get Brexit done” – was dishonest and a con. “In towns where the steelworks have closed, politics as a whole wasn’t trusted. But Boris Johnson’s promise to get Brexit done – sold as a blow to the system – was. Sadly that slogan will soon be exposed for the falsehood it is, shattering trust even further.”

He also savages the media for its criticism of Labour under his leadership and says the party must do more “to meet this billionaire-owned and influenced hostility head-on”.

But as Labour tried to come to terms with its heaviest election defeat since 1935, an increasing number of MPs and candidates who lost their seats tore into Corbyn and his inner circle of advisers.

Harriet Harman, responding on Twitter to Corbyn’s Observer article, called on him to step down immediately. “This shows no willingness to understand why @UKLabour suffered this catastrophic defeat,” she tweeted.

This shows no willingness to understand why ⁦@UKLabour⁩ suffered this catastrophic defeat. ⁦@jeremycorbyn⁩ should resign. We won the argument, but I regret we didn’t convert that into a majority for change | General election 2019 | The Guardian https://t.co/FXbn77Vfmr — Harriet Harman (@HarrietHarman) December 14, 2019

Peter Kyle, who held on to Hove and Portslade, said Corbyn and his allies could not depart the stage soon enough.

“They’ve been waging an ideological and personal war for decades and must now leave others to build a movement fit for the future, rooted in the future, and capable of carrying Labour to power in order to shape the future,” Kyle writes in the Observer.

“Voters also said we needed to look more competent, questioning how a party that can’t manage antisemitism out of its own party could possibly run the Home Office.”

Wes Streeting, who retained Ilford North, said it was necessary that Corbyn and his allies should “own the defeat” and be held fully responsible for it.

But he stressed the need to find a successor as fast as possible. “The urgency arises from local elections next May. If we give the impression that it is business as usual, then decent, hard-working Labour councillors will suffer the same fate as Labour candidates did on Thursday and we cannot allow that to happen.”

Today in the Observer two likely candidates in the battle to succeed Corbyn, Jess Phillips and Lisa Nandy, spell out their ideas on how Labour can rebuild trust and become more open to ideas from all wings of the party.

A spokesman for Corbyn said a timetable for the leadership contest would be decided by the national executive committee, possibly as early as this week. The contest is not expected to start until next month. “There is a feeling that we don’t really want to be starting a leadership contest over Christmas,” he said.