George Osborne has admitted the Conservative government “didn’t spot the shift in politics” that led to the leave vote in the EU referendum, saying it had failed to fix the banking system or explain the positives of immigration or the EU.

The former chancellor, who edits the Evening Standard, said his party “did get things wrong” in the run-up to the 2016 vote, including promising a net migration target – of tens of thousands – that could not be delivered.

“I think we were wrong to play into the debate that everything that Brussels did was a challenge and a battle,” he told Newsnight. “We were too late in the day trying to explain some of the benefits of European Union membership.”

He said David Cameron’s pledge that net migration would be below 100,000 was not possible to deliver and would not be delivered in the future, but suggested that had led to claims that leaving the EU would be the only way to meet the target.

“We definitely contributed to that argument. We didn’t make enough of the value of immigration,” he said.

Osborne said that argument had then been used by a minority of leave supporters who were convinced by the “rather esoteric issues of constitutional sovereignty”, which had not previously been an issue of major public concern.

“We allowed that kind of minority concern – because we pool sovereignty in all sorts of different organisations like Nato – to be linked to immigration control. And that was pretty lethal in that referendum debate,” he said.

During the interview, Osborne defended his decision to make £12bn in welfare cuts, though he did not specifically address whether the cuts were too much.

Play Video 1:30 Polly Toynbee tells George Osborne he was most rightwing chancellor ever – video

“It would be a bit odd to leave out the very large chunk the government was spending on welfare,” he said of his austerity measures.

He said Philip Hammond’s budget, in which the chancellor said the era of austerity was coming to an end, was “a perfectly natural end point to the repair job on the public finances”.

Osborne said he was deeply concerned about the future of the Conservative party, which he said had fuelled his personal criticism of the prime minister, whom he has previously called “a dead woman walking”.

He said: “I worked very hard all my life to make the Conservative party electable. And it’s painful to me to see it losing support in large areas of the country where it shouldn’t be – particularly against a Labour opposition that I don’t think is in a fit state at the moment.”

He said his party had won previous elections by being “socially progressive and fiscally conservative” but in the last election had “tried to out-Ukip Ukip” which he blamed for the loss in support.

“We ain’t going to win the next election by trying to out-Corbyn Corbyn,” he said of the Labour leader.