Rishi Sunak has acknowledged he is “playing catch-up” to Liz Truss as he seemingly claimed the Tory leadership race’s sought-after underdog status.

The 42-year-old alluded to the fallout from his wife’s tax status when he appeared to suggest some commentary claimed he “wouldn’t even have been a part of this contest” if she had not announced her decision to pay UK taxes on her overseas income while he was still chancellor in April.

As the Foreign Secretary continued to best him in the polls, Mr Sunak’s weekend has been characterised by his pledge to end “woke nonsense” and his supporters attributing his unpopularity to “latent racism” – a claim which he was quick to dispute as incorrect.

In an interview with The Sunday Telegraph, Mr Sunak also revealed his plan to reform the NHS would include a temporary £10 fine for patients who fail to attend a GP or outpatient appointment.

“If we have people who are not showing up and taking those slots away from people who need it, that’s not right,” he told the newspaper. “I’m all for a healthcare system that’s free at the point of use, but not one that’s free at the point of misuse.”

He added: “Yes, it means we have to do something brave and something different, but that’s what I’m about doing. I want to be a transformational prime minister.”

When such proposals have surfaced in the past, doctors have warned that a system of fines could create a new layer of bureaucracy with which GP surgeries would struggle to cope.

Meanwhile, Ms Truss played down claims she has a clear lead over Mr Sunak, even as her campaign was further buoyed by endorsements of party heavyweight Tom Tugendhat, insisting it was a “very, very close race,” while trumpeting her “support from right across all parts of the Conservative Party”.

Earlier on Saturday, in another bid to revive to his flagging premiership, the former chancellor vowed to slash the number of empty shops on Britain’s high streets and crack down on graffiti and littering.

Mr Sunak also pledged to expand police powers to tackle anti-social behaviour in public spaces.

Under his plan to rejuvenate high streets, many of which are blighted by shuttered shops and derelict buildings, Mr Sunak would remove hurdles for those properties to be quickly converted into new businesses or cafes.

He would allow local authorities to double the fine for littering and graffiti and consider lowering the damage threshold for offenders to be jailed.

Mr Sunak would strengthen orders that allow police to disperse people behaving anti-socially, and extend the powers to apply to types of behaviour rather than just a location.

He would also seek to reduce regulations around farmers markets, make local authorities assess social value when considering the location of public services, and protect access to cash points.

Mr Sunak said: “I want to slash the number of empty shops by 2025 and make sure that they are turned into thriving local assets, supporting skills, local businesses, economies and creating jobs.

“They will be joined by vital public services – like police stations and job centres.

“I’ll also support covered markets and farmers markets, making it as easy as possible for them to trade on our high streets and sell their fantastic produce to local people.

“We should all take pride in our high streets so I will also crack down on anti-social behaviour, graffiti and littering – through extended police powers and increased fines.

“I have been clear that I have a plan to rebuild our economy; our high streets are a crucial part of that.”

Mr Sunak and his rival in the race for No 10 have faced calls from a group of the UK’s biggest retailers to cut business rates.

The Retail Jobs Alliance – which includes Tesco, Greggs and Sainsbury’s – last week accused the candidates of failing to prioritise the high street as companies are being hammered by the so-called shops tax amid spiralling inflation.

CBI director general Tony Danker has also called for an urgent reform of the business rates system.

As chancellor, Mr Sunak provided business rates relief during the pandemic and oversaw a review into the property tax, but no radical reform followed.

Ms Truss has signalled she would overhaul business rates if she becomes prime minister.

A BMG Research poll of party faithful for the i newspaper was the latest to put Ms Truss ahead of Mr Sunak with a double-digit lead, a survey of Tory councillors saw the two contenders nearly neck-and-neck.

Ms Truss was on 31% and Mr Sunak on 28% among 511 local Conservative politicians polled by Savanta ComRes.