Thank you all for your advice etc.. The AA man came (after I'd cleaned the fuses (and found one had blown!) and he couldn't make it work either, but in fiddling with it, we managed to turn the immobiliser off.
Thanks also to POWARTEK for the inspirationally nihilistic approach but alas the Rover Minis of 1995 were super security concious and the thing is wired into the ECU and stops transmission AND running!
However there is a good specialist on Canvey Island who has quoted ÃƒÆ’Ã¢â‚¬Å¡Ãƒâ€šÃ‚Â£119 for a complete new unit (that they can fit tomorrow afternoon)
TRhen it's off the my Mini specialists to look at the oil leak - bloody speed bumps . . . . . .