King Henry actually was very close with his son Henry, choosing to have him raised in his close friend Becket's home - a common practice for royalty in that era. The prince's resentment over his father's possible causation of Becket's death (intentional or not) was a major reason he became distanced from his father in later years, although the prince eventually died six years before his father.
Empress Matilda (Maud), King Henry's mother, had been chosen by her father King Henry I to rule after his death; but the ruling Council of England decided it would be inappropriate for a woman to rule, and named her cousin Stephen as king. This set off decades of war, during which Matilda captured much of western England and was proclaimed Lady of England. Though she never became queen, she successfully established her son Henry's claim to the throne. She died in 1167, three years before Becket's murder.
The closeness between King Henry and Becket is depicted as being a purely platonic one. Homosexuality was illegal at the time in Britain and any suggestion of that would have fallen foul of the censor.
Queen Eleanor was in actuality perhaps the wealthiest and most powerful woman in Europe, and hardly the figure portrayed in the play. Although here she remarks that she will complain to her uncle the emperor, she was not related to Frederick Barbarossa. Complaining to Frederick would have been awkward for a devout Catholic anyway, as he had himself been excommunicated in 1160 and was in a power struggle with the pope, establishing several rival antipopes before reconciling with Rome in 1177. Eleanor also says she will protest to her father, but her father died when Eleanor was 15, long before she met Henry.
A point not mentioned in the play is that Queen Eleanor's first marriage had been with King Louis VII of France; the marriage was later dissolved for reasons of common ancestry, although Henry was exactly as close a relation as Louis had been.
Becket's tomb became a popular destination for pilgrimages for centuries, but it was looted and destroyed in the early 16th century in the Dissolution of the Monasteries during Henry VIII's reign, as part of the Church of England's break from Rome. A shrine was later created at the site.
Originally produced on Broadway in 1959 with Laurence Olivier as Becket and Anthony Quinn as King Henry. When Quinn left the play to make films, Olivier took over the role of Henry and Arthur Kennedy was brought in to play Becket.
The original Broadway play on which this filmed production is based opened at the St. James Theater in New York on October 5, 1960 and ran for 193 performances. Its script "Becket" by Jean Anouilh (as the basis for the screenplay) won the 1961 Tony Award (New York City) for Best Play.
Richard Burton claimed to have been offered either of the main roles. However, according to the producers this was not true, since Peter O'Toole had already been cast as Henry II and Becket had to be the older man. Burton was seven years older than O'Toole.
While it won a screenplay award, this film still holds jointly a record for the most Oscar category losses - 10. The other joint holders with 10 category losses are The turning Point, The Colour Purple, Gangs of New York, and True Grit.
At the beginning of the DVD commentary, O'Toole relates his meeting with Anouilh in Paris a few years before the film was made because he was being considered for the play. Anouilh told him that he had been looking for an idea based on a rift in the leftist Théâtre National Populaire between the actors Gérard Philipe and Daniel Ivernel. He visited Canterbury and decided the Becket story would be a good vehicle. Philipe and Ivernel were cast as Becket and Henry respectively for the Paris premiere of the play, but Philipe died during rehearsals.
In the DVD commentary for the MPI release of the restored version of "Becket," Peter O' Toole said he "got on well" with producer Hal Wallis. O' Toole was particularly interested in asking Wallis about Elvis Presley who was then starring in such Wallis produced films as "Blue Hawaii" (1961) and "Girls! Girls! Girls!" (1962) which shared a screenwriter, Edward Anhalt, with "Becket."