In To Sir, With Love, did Gillian's parents approve of her relationship with Rick?
Chapter Twenty-One of this excellent account of one black teacher's struggle for acceptance is the chapter you will want to re-read to answer this question. It details the first time that Gillian took Rick back to her parents' home to be introduced to them. Gillian's father at this stage has a very frank talk with Rick, in which he says to him that he would rather Gillian had fallen in love with somebody her own colour:
We would, even now, prefer that Gillian had fallen in love with someone of her own colour; it would have made everythign so much easier for her as well as for us... It's not just the two of you, Rick, that have to be considered. You might have children; what happens to them? They'll belong nowhere, and nobody will want them.
However, in spite of these concerns, Gillian's father is also very open about the fact that he likes Rick and does not find anything wrong with him apart from the concerns that he has about the impact of his skin colour on his daughter and their future together. Thus, although he has his reservations, we can see this as being a result of racism in Britain at the time rather than any particular problems with Rick as an individual as far as his character goes.