Welcome to the club, Danny.
I have had an S Type 2.7 d for the last 7 years, and like you, are thoroughly enjoying Sir William Lyons' "Grace, Pace and Space".
I have only had one minor issue with the XF gearbox and that was when I was using the manual system to slow the engine down on downhill roads. I have had auto gearboxes for 18 years and this is the only issue I have had.
I am not an expert in the mechanics of a car, but I do know of a company that is expert on gearboxes. Unfortunately it is in Scotland. I would google around and see if there is someone like that in the South of England.
Good Luck,
Peter.