thanks for all your replies folks!
Following your advice, I've checked there is 240v going to where it should (!) so now need a trustworthy gas engineer to have a look: the guy who checked it (and should have serviced it) as part of the Exchange of Contract conditions seems to have...
My son has just bought a flat in Putney which has a Baxi Bermuda installed. The fire works fine but the pilot light for the back burner goes out when I release the grey button. Any suggestions? Thanks!