Well, I've finally got around to having "the conversation"!
I nearly chickened out completely, to be honest. But in the end I managed to say "There's something I've got to tell you..." and it all came out (and so did I).
They were not even slightly surprised, but they were concerned, especially about surgery. And my Mum had a weepy moment about "losing me", but I reassured her that the essential "me" would not change.
The main thing that helped, I think, was that I told them that they would know what was happening every step of the way, and that I would not keep them in the dark. And I also said that if they had any concerns at all or wanted to ask me any questions, they had only to text me and I would pop over and discuss it with them.
Phew! That's the worst pre-transition job done, now. My work know, some of my friends know, my family knows, and my partner knows. Onwards and upwards...!

Gil