Just had a phone call from British Gas customer services (genuine caller, not a scammer). My original complaint was being looked into by their residential department. He confirmed that the calls I'd been getting were nothing to do with British Gas. He wasn't able to say what their intent was.
Having received a similar scam call the other day, I reported that one which is currently being looked into by British Gas Business. I asked the person who rang me just now to pass my comments on to them.
These calls seem to be targeting small businesses. The callers are reading from a script, they either ask for the manager or use your business name. They say that your contract (seems more likely to be electricity rather than gas) is up for renewal. They will claim to be British Gas or another supplier (which may or may not be yours). What they are wanting you to do is to make some sort of confirmation with the intent on sending you paperwork.
I think if you get such a call challenge them to tell you some of the digits in your account number as they won't be able to answer as they don't know.