Two of the most significant voices to have waded into the row are former prime ministers John Major and Tony Blair, who have condemned the show's depiction of them.
Sir Tony was particularly scathing of one element, which shows Charles trying to recruit him as an ally to protect his future and pave the way for him to marry Camilla shortly after the 1997 general election.
He said of it: “It should come as no surprise that this is complete and utter rubbish.”
Watch: The Crown in hot water over ‘nonsense’ Charles scene
It is, naturally, very difficult to peek behind the curtain when it comes to the royal family's relationships with politics and politicians.
Queen Elizabeth II, of course, was constitutionally bound by political neutrality. That meant she remained pretty tight-lipped about her personal views and thoughts on the 15 prime ministers that served in her name.
What she really thought about them has long been a matter that has attracted a high level of speculation. The weekly private audiences with the monarch have been said to be one of the only situations that prime ministers are free to be totally candid.
Yahoo News UK runs through the brief glimpses we've had into what Queen Elizabeth really thought about them.
The Queen has reportedly admitted that of all her prime ministers, Winston Churchill was her favourite. When asked, she is widely quoted as saying: "Winston, of course, because it was always such fun."
However, it was not always plain sailing, with the late Queen also quoted as saying when she was asked if Churchill was mentoring her: "Not at all, I find him quite obstinate."
Overall, the Queen thought highly of her first prime minister, who had also served under her father, King George VI. She recommended he should have a state funeral — Churchill was the first non-royal to receive this honour in 30 years and the first politician to receive it in a century. The Queen also attended his funeral, something she only did for two prime ministers.
Queen Elizabeth wrote when giving permission for the state funeral to take place: "I know that it will be the wish of all my people that the loss we have sustained [...] be met in the most fitting manner and that they should have an opportunity of expressing their sorrow."
Churchill — who the Queen also called "an inspiring leader" and an "outstanding man" — seemed to think as highly of the monarch. He is quoted as saying of Queen Elizabeth, "all the film people in the world, if they had scoured the globe, could not have found anyone so suited for the part."
It is relatively unknown what the Queen thought of her second premier, who oversaw a couple of significant crises in his relatively short time as prime minister.
The Queen's sister, Princess Margaret, wanted to marry Group Captain Peter Townsend who had worked as her father's equerry. However, she needed the Queen's permission to marry and as Townsend was divorced, it sparked a crisis.
With the Queen as Supreme Governor of the Church of England, there was a conflict between her sister's wishes and the teaching of the Anglican Church.
Eventually it was decided that Princess Margaret and Townsend would not get married, but then Anthony Eden was faced with another challenge — the Suez crisis — shortly after which Eden resigned.
The Queen's third prime minister was Harold Macmillan, and she is said to have eventually enjoyed a good relationship with him.
After Eden's resignation in 1957, the Queen took advice from the Conservative Party and invited Macmillan to become Prime Minister. This was the penultimate time what was called the "Queen's prerogative" to choose was ever used.
It is likely Queen Elizabeth thought highly of Macmillan as she sought his counsel and advice many times after he had left office.
The Queen's prerogative to choose was used for the final time in 1963 with the appointment of her fourth prime minister, Alec Douglas-Home. Douglas-Home was a long time friend of the Queen Mother, and so the Queen knew him in a personal capacity as well.
Perhaps it was because of this personal tie that the Queen attracted some criticism, but Douglas-Home's appointment was "based on a memorandum from the retiring prime minister" rather than any personal preference of the Queen.
Douglas-Home served as premier for only one year, but remained close with the Queen, even helping her name some of her horses.
In 1964, the Queen had her first Labour Prime Minister — Harold Wilson. The two were said to have got on very well, with Wilson particularly enjoying his trips to Balmoral where he saw a more informal side to the Royal Family.
He said that he enjoyed a "relaxed intimacy" with the Queen, the two were only a decade apart in age, with Wilson being far younger than his predecessors. It is said that after just their first audience the Queen invited him to stay for a drink.
It has also been reported that such was his affection for the Queen that he carried a photograph of "himself with her around in his wallet until it almost disintegrated."
Edward Heath and James Callaghan
Edward Heath — the Queen's sixth prime minister — oversaw a turbulent time in British politics with the Troubles of Northern Ireland reaching new highs, the miner strikes and electricity blackouts to name a few.
The two reportedly shared relatively opposing world views, and in Ben Pimlott's book Elizabeth II and the Monarchy a source revealed the Queen "was never comfortable with him."
Equally, Heath is reported to have found his private audiences with the monarch "frosty."
The Queen would presumably have had an easier time with Callaghan, who was a committed monarchist. Callaghan's premiership lasted from 1976-1979.
Not much is known of the Queen's opinion of Callaghan but he said of the monarch that she was "able to see the funny side of life," and that she "provided friendliness, not friendship to her prime ministers."
Thatcher was the Queen's — and the United Kingdom's — first female prime minister. It was widely reported during her premiership that she did not get on with the Queen.
However, in her autobiography, Thatcher wrote that these claims were unsubstantiated: "Stories of clashes [...] were too good not to make up."
However, the two women did reportedly disagree over sanctions on apartheid South Africa. Michael Shea — the Queen's former press secretary — spoke "without royal assent to a Sunday Times reporter" on this topic which led to a controversial article about the late Queen being "dismayed by uncaring Thatcher" being published.
Bound by political neutrality, the palace hastily distanced itself from the article, but the Queen's "warm friendship" with Nelson Mandela — who addressed her by her first name and in letters referred to her as "my dear friend Elizabeth" — might indicate the report at least somewhat accurately expressed her views on the Apartheid regime.
After Thatcher's long premiership finally ended, John Major replaced her and became the Queen's ninth prime minister.
Major oversaw a turbulent time in the House of Windsor, which included the Queen's annus horribilis of 1992 during which three of her children's marriages ended, Windsor Castle caught on fire and there were a myriad of public scandals.
He has spoken very highly of the Queen, calling her "selfless and wise." After the death of Diana, Princess of Wales in 1997, Major was given the position of "special guardian" to her two sons William and Harry.
Tony Blair and Gordon Brown
Blair was, it has been reported, the Queen's least favourite prime minister. His decade-long premiership began with the untimely death of Diana, and it is said he encouraged the Queen to make a public statement of grief at the time, something that she had not initially wanted to do.
The Queen is said to have disliked the "people's princess" title that Blair assigned to Diana.
Gordon Brown took over from Tony Blair in 2007, and he referred to the relationship he shared with the Queen as "congenial and businesslike."
It has been reported the Queen "admired Brown's diligence and seriousness".
However, neither Brown nor Blair were invited to the royal wedding in 2011 of Kate and William.
David Cameron and Theresa May
Cameron certainly had a leg up compared to his Labour predecessors as a distant relative of the Queen. He also attended the same school as Prince Edward, a couple of academic years below. The first time the late Queen came across him was "in a primary school play."
However, his indiscretion after the Scottish Independence Referendum in 2014 may have soured relations.
Cameron was forced to apologise for comments he made about the Queen's reaction to the referendum's results.
Whilst wearing a microphone, he said: "the definition of relief is being the prime minister of the United Kingdom and ringing the queen and saying 'it's all right, it's okay.' That was something, she purred down the line."
Theresa May's premiership was blighted by repeated attempts to secure a Brexit deal.
The Royal Editor of ITV — Chris Ship — has said that he had heard some members of the Royal Family "speak with admiration for the level of hard work and many hours of negotiation Theresa May" displayed during her time as prime minister.
Boris Johnson and Liz Truss
Johnson had to apologise to the Queen twice, and reports have claimed that she "loathed" him.
His first indiscretion came when he claimed she had said in one of their weekly audiences she didn't "know why anyone would want the job" of premier.
Johnson's first apology to the Queen came after he supposedly misled her on the legality of proroguing parliament in 2019.
Later in January 2022, Johnson was forced to apologise again after it was revealed that illegal parties had been held at Downing Street the night before Prince Philip's funeral.
Liz Truss was the Queen's 15th and final prime minister.
Inviting Truss to form a government at Balmoral only two days before her death, it will be remembered as the Queen's final significant act of constitutional duty.