I would have thought that any good local tyre dealer should be able to direct you to someone who can do it.
There is also info you might like to have on
www.mgb-stuff.org.uk/wheelstext.htm scroll down to wheel balancing.
Hope this is helpful. David

Hi Pete
The man you need to talk to is Ian Wallman MG Owners Club. telephone 01954 234001 when i rang him he quoted me £7-50 per wheel , and he does have the right equipment . They are at Swavesey nr Cambridge , hope that helps . regards Eric

Thanks for that Eric. I have contacted them and they are happy to do the balancing, at the price you mentioned.