Although Christine Keeler was denied membership of Actor's Equity, the union was less censorious about Mandy Rice-Davies, who eventually did become an occasional actress in small film and TV roles many years after the Profumo Affair.
It is quite true that the real Christine Keeler was, as shown in this episode, approached to play herself in a cheap exploitation movie about the Profumo Affair and was refused membership of the Actor's Equity trade union, causing the project to be abandoned. However, there was a film made about the affair in Denmark, with Yvonne Buckingham playing Christine Keeler and John Drew Barrymore playing Dr. Ward. The film (variously entitled "The Keeler Affair" and "The Christine Keeler Story") was in American cinemas before the end of 1963, although it was banned in Britain and has never been seen there legally. The real Christine Keeler filmed a brief introduction for it.
The real Mandy Rice-Davies did very well out of the Profumo Affair, and became a successful club- and bar-owner in Israel, where she lived for many years. She became a well-known and popular public personality in that country. She eventually returned to England, and even claimed that she had become quite friendly with Margaret Thatcher. She died at age 70 in 2014. Christine Keeler, however, was never able to move on from the scandal, or put it behind her; she endured a life of considerable hardship, for the most part. Decades after the affair, when she was well into middle-age, she was sacked from a poorly-paid job as a school dinner-lady after her identity became known to the school governors. Both her marriages were short-lasting and ended in divorce. She died in 2017, aged 75.
The script perpetrates a blatantly obvious grammatical howler in the scene where Profumo and his wife are making a statement to the press - he says "you are asking for a comment from my wife and I", rather than "my wife and me". No upper-class Englishman of Profumo's generation would have made such a mistake, and it's rather shocking to think that a BBC scriptwriter would have.