As said, it's normally the regulator when these fail, and that's simple to change, but results in the car being off the road for longer than a simple alternator swap, unless you know the style of regulator and get hold of one in advance. IIRC the style of alternator changed around the facelift time, or possibly when the 2.5/3.0 engines were phased out.
If you can get hold of a 2nd hand alternator, you can swap it and then fit a new regulator to the old one so you have a spare. Regs are cheap - only £20 or so.
If James can't sort it and you can get your hands on a replacement I may have some time to spare early next week.
The other thing that occurred to me is that an auto electrical specialist might be a better bet, as they will be able to take it off the car, test it, fit a new regulator and replace rather than just fit a new whole alternator. There always used to be a place behind the garage on the A340 in Sherborne St. John. It sticks in my mind as he always had an Omega outside. Might be worth a try?