I’m sure there must be a company around Nottinghamshire, maybe CAT auto keys that can supply and programme a replacement 3 button 433mhz remote for around £42-£85. BMW/MINI dealership £130-£200
I’m sure it’s an easy replacement if the original fob is damaged, and would appear not to cost an arm and a leg, obviously avoid BMW/MINI parts department part is cheap, but it’s the labour to cut the key or use old key and have fob programmed to car,1/2 hour to an hour labour.