Well I have an update...
I followed bigblue75's advice and bought a genuine MG Rover part (XKB000022A). I've fitted it and the brake lights now work as they should. Sir, I am in your debt!
The first switch I bought was from Eurocarparts. I will be getting in touch with them to tell them the part doesn't work with our cars.
Thanks again everyone - I'm not sure what I would have done without the help of this forum. I'm now going to have a celebratory beer!