Hackney MP Ms Abbott has since responded, saying the Tory donor's reported comments had put her in a "frightening" position.

But who is Mr Hester and what is he alleged to have said about Ms Abbott?

How Mr Hester made his fortune

The 58-year-old healthcare entrepreneur is founder and chief executive of The Phoenix Partnership (TPP).

Based in Leeds, TPP describes itself as "a leading global provider of healthcare technology".

It says it provides "vital clinical IT services in... more than 2,600 GP practices".

During the pandemic, it was reported to have won a six-figure contract to supply data on vaccine uptake levels.

Mr Hester, who was awarded an OBE in 2015 for services to healthcare, made last year's Sunday Times Rich List with an estimated fortune of £415m.

He was a computer programmer when he founded TTP in 1997 and was listed as one of the UK's top 50 innovators in the national health publication Health Service Journal in 2013.

Huge donations to the Tories

Mr Hester donated £10m to the Tories last year, including a £5m donation to Rishi Sunak that came from him personally and another £5m that came from his healthcare software firm in November, Electoral Commission records show.

His ties to the party go back a long way.

In 2013, he travelled to India with David Cameron, the then-prime minister, as part of what was Britain's biggest-ever trade delegation.

"This trip is worth a lot of money to us - it's invaluable," Mr Hester reportedly told the Financial Times during the trip.

"Being with the PM and UK Trade and Investment means we [see] the right people."

The following year, Jeremy Hunt, the then health secretary, visited TPP's headquarters, saying: "Technology is the key to 21st century personalised healthcare, so it is great to see companies like TPP leading the way with new software that will put [care home] residents in control of their health."

What were his alleged remarks about Ms Abbott?

According to The Guardian, Mr Hester made remarks about Ms Abbott in 2019 during a meeting at his Leeds company headquarters.

In an article published on Monday, the publication reported he said: "It's like trying not to be racist but you see Diane Abbott on the TV, and you're just like… you just want to hate all black women because she's there.

"And I don't hate all black women at all, but I think she should be shot."

How has Mr Hester responded?

A spokesperson for the entrepreneur released a statement saying: "Frank Hester accepts that he was rude about Diane Abbott in a private meeting several years ago but his criticism had nothing to do with her gender nor colour of skin.

"The Guardian is right when it quotes Frank saying he abhors racism, not least because he experienced it as the child of Irish immigrants in the 1970s."

It added: "He rang Diane Abbott twice today to try to apologise directly for the hurt he has caused her, and is deeply sorry for his remarks.

"He wishes to make it clear that he regards racism as a poison which has no place in public life."

How Ms Abbott responded

In her own statement, Ms Abbott, the UK's first black woman to become an MP, detailed how "alarming" the alleged remarks were in light of the murder of two politicians since 2016.

"It is frightening," said Ms Abbott. "I live in Hackney and do not drive so I find myself, at weekends, popping on a bus or even walking places more than most MPs.

"I am a single woman and that makes me vulnerable anyway. But to hear someone talking like this is worrying."

She added: "For all of my career as an MP I have thought it important not to live in a bubble, but to mix and mingle with ordinary people. The fact that two MPs have been murdered in recent years makes talk like this all the more alarming."

PM's spokesperson says comments 'unacceptable' but ministers refuse to call them racist

Asked about the reported remarks at a regular briefing with journalists, Rishi Sunak's spokesman said they were "clearly unacceptable", but refused to say if they were racist.

Energy minister Graham Stuart told Sky News the remarks were "truly awful".

The PM's spokesperson referred to Mr Stuart's comments as he said: "I wouldn't usually comment on alleged words, second-hand accounts, etcetera.

"But, as minister Stuart said this morning, what is alleged and reported to have been said is clearly unacceptable."

He refused to be drawn on why they were unacceptable, adding: "I don't have anything to add beyond what minister Stuart said this morning."

Work and Pensions Secretary Mel Stride also told broadcasters the comments were "inappropriate", but added: "I think the critical point here is I don't think what he was saying was a gender-based or a race-based comment."

Conservative MP and former chancellor Kwasi Kwarteng, however, said that the reported comments were "clearly racist and sexist".

Calls for funds from Mr Hester to be returned

Sir Keir Starmer, London mayor Sadiq Khan and other political opponents of the Tories have demanded that the party return the money Mr Hester donated.

The Labour leader told ITV's Lorraine: "The comments about Diane Abbott are just abhorrent.

"And Diane has been a trailblazer, she has paved the way for others, she's probably faced more abuse than any other politician over the years on a sustained basis.

"And I'm sorry, this apology this morning that is pretending that what was said wasn't racist or anything to do with the fact she's a woman, I don't buy that I'm afraid, and I think that it's time the Tory party called it out and returned the money."

The PM has not directly commented on the demands, nor has the Conservative Party.

Asked if the party should return Mr Hester's donations, Mr Stuart said: "We can't cancel anybody from participation in public life, or indeed, donating to parties because they said something intemperate or wrong in their past."