Sir Michael became manager of the Royal Studs in 1970 and stayed in the role for almost 30 years.
He was the Queen Mother’s racing manager and then became jumps adviser to Her Majesty after her mother’s death.
John Warren, the Queen’s racing adviser, told the Racing Post: “Sir Michael did a magnificent job managing the Royal Studs for so long.
“He was deeply committed to the studs, the Queen, and the Queen Mother.
“He was extraordinarily enthusiastic and got such a buzz out of all the royal winners.”
Nicky Henderson, a horse trainer, said Sir Michael had “the most amazing twinkle and such a lovely impish air about him”.
He added: “He really was the most lovely man and came out with such wonderfully witty lines.
“He had a marvellous military background and always referred to his wife, Lady Angela, as the commanding officer.
“He was very close to the Queen and the Queen Mother and loved his role with their horses.”
Sir Michael was appointed Knight Grand Cross of the Royal Victorian Order (GCVO) in the 2020 New Year Honours list.
The Royal Family are known to be fond of equestrian sports. The Queen learned to ride a horse at the age of three.
Prince Philip also played polo until 1971, then he discovered carriage driving and continued to drive his ponies around royal estates into his 90s.
Princess Anne and Zara Tindall have both competed at the Olympics in Eventing.
And Lady Louise Windsor has also followed in her grandfather’s footsteps to become an accomplished carriage driver.