She rode alongside Her Majesty on the way to the Diamond Jubilee service in 2012 when Prince Philip was too ill to attend.
Lady Farnham, whose name was Diana Maxwell, also accompanied the couple on royal tours during her 44 years of service for the Queen.
A royal source told The Telegraph: "It is very sad for the Queen. Everyone loved Lady Farnham, she was always so good-humoured. She was also a very glamorous and attractive woman.
"She was always very generous to new people joining the household.
"It has not been a good year for the Queen – losing her husband and then the Duchess of Grafton and now Lady Farnham.
"They were dear friends who supported the Queen on official duties. Unfortunately a sad consequence of living a long life is that you have to say goodbye to a lot of people you care about."
Another of the Queen's close friends, the Duchess of Grafton, Ann Fortune FitzRoy, died at the start of December.
She served as the Queen's Mistress of the Robes from 1967 until her death at the age of 101.
The Queen is also still mourning her husband Prince Philip, who died last April aged 99.
She was moved viewers to tears on Christmas Day while making reference to her beloved husband in her annual speech.
The monarch said: "Although it's a time of great happiness and good cheer for many, Christmas can be hard for those who have lost loved ones.
"This year, especially, I understand why.
"But for me, in the months since the death of my beloved Philip, I have drawn great comfort from the warmth and affection of the many tributes to his life and work – from around the country, the Commonwealth and the world."