The UK should follow Scotland’s lead on raising taxes to avoid spending cuts and austerity, SNP leader John Swinney has said.

He told the BBC’s Nick Robinson that Labour had “signed up” to £18bn of cuts planned by the Conservatives – a claim denied by Sir Keir Starmer’s party.

Mr Swinney said higher tax rates, like those in Scotland where anyone earning above £28,850 pays more than elsewhere in the UK, would close that fiscal gap.

He urged Scottish voters to back the SNP because it was “crystal clear” Labour would win in England and his party would best protect Scotland’s interests at Westminster.

The £18bn figure quoted by Mr Swinney is a reference to work by the Institute for Fiscal Studies (IFS).

IFS research economist Bee Boileau has described it as a “fair assessment” of the kind of cuts some UK government departments might face each year by the end of the next parliament – although she added there was some uncertainty about their precise scale.

Mr Swinney accused Labour of “not being open with people” about the financial pressures that were coming down the line.

Asked what he would do if he were prime minister, he said: “I would replicate the tax changes we’ve made in Scotland in the rest of the UK and that would essentially address the £18bn fiscal gap.”

In Scotland people earning below £28,850 pay slightly less tax than the rest of the UK but above that figure they pay increasingly more.

Someone on £50,000 in Scotland, which includes some teachers and police officers, pays £1,542 more than they would in the rest of the UK. That rises to £3,346 for someone on £100,000.

Mr Swinney said those who paid the extra tax benefited from things such as free university tuition and free prescriptions as a result.

Responding to Mr Swinney’s claims about Labour being committed to Tory cuts, Shadow Scotland Secretary Ian Murray insisted “there will be no austerity under Labour”.

He said Labour would “deliver economic stability, treat public finances with respect and give public services a badly needed funding boost”.

Mr Murray added: “We will raise specific taxes for those with the broadest shoulders to put an immediate injection of cash into public services, and grow our economy to put our country’s finances on a sustainable footing in the long-term.”

Until a few weeks ago, Mr Swinney had stepped back from frontline politics but the resignation of Humza Yousaf propelled him from the backbenches at Holyrood into the top job in Scottish politics.

An SNP stalwart, he first held office when the SNP came to power 17 years ago.

During the interview he was shown a photo of him with Nicola Sturgeon and Alex Salmond, and was described as one of the “three musketeers of the SNP”.

He was asked if he really represented the change of political leadership that a recent poll suggested many voters were seeking.

“I think what the people are saying is that they’re concerned about the issues that affect their lives, about the cost of living, about the challenges of their public services, about the implications of Brexit, for example,” he said.

Mr Swinney accepted his party had gone through a “tough time” with three leaders in two years, a police investigation into party funds and criticism of its record on education and the NHS.

“That’s why I’m here. I’m here to sort it out, to strengthen the SNP and to build the trust with the electorate – and that’s exactly what I’m doing,” he said.

Mr Swinney was challenged on his pursuit of Scottish independence which some analysis suggests could intensify the austerity he has warned against.

The IFS – the same organisation whose figures he has used to attack Labour – has predicted an independent Scotland would have to impose bigger spending cuts or tax rises in its first decade

The SNP leader replied that an independent Scotland would have “more flexibility and manoeuverability to improve our economic performance”.

He also restated his position that a simple majority of MPs in Scotland would be a mandate to open “immediate negotiations to bring about independence”.

But he said “everyone accepts” the “best way to go about this” is through a second independence referendum.

The SNP leader was also pressed on an apparent softening of his party’s position on granting new oil an gas drilling licences in the North Sea.

It is a power reserved to Westminster and Labour has proposed a ban on granting new licences.

One of his predecessors as first minister, Nicola Sturgeon, described the granting of a licence for the Rosebank field by the Conservatives as the “greatest act of environmental vandalism of her lifetime”.

But Mr Swinney said new applications should be considered on a “case-by-case” basis and assessed to see if they were compatible with climate change objectives.

While not ruling out support for some new licences, he criticised the scale of Conservative backing for further exploration.

“The prime minister has basically said he will license 100 new projects. I think that is utterly irresponsible,” he said.

“That is climate denier status of the first order.”

At the same time he said he was not prepared to allow the oil sector in north east Scotland be devastated in the manner of Scottish heavy industry when Margaret Thatcher was in power in the 1980s.

Mr Swinney was also asked about the amount of effort and time that had been spent on legislation making it easier for people to change gender.

A new law was passed at the Scottish Parliament but blocked by the UK government on grounds that it impacted on the UK-wide equality legislation, a position later upheld by the courts.

Mr Swinney said it was up to the incoming government to decide if it would maintain its opposition to the Scottish legislation.

“We’ve got to be absolutely focused making sure that we protect the rights of women and girls as we wrestle with all theses issues,” he said.

But he said the “great challenges” facing the transgender community also have to be understood.

“I want to bring people together,” he said.

The BBC is interviewing all the major party leaders in the run-up to the election in The Panorama Interviews with Nick Robinson. You can watch the interview with John Swinney at 19:00 on BBC One or BBC iPlayer.