Interesting question… You could send a Data Protection Notice to British Gas to stop the unsolicited phone calls. Section 11 of the Data Protection Act gives you the right to ask any UK organisation to stop (or not begin) processing your personal data for purposes of 'direct marketing'. The section defines 'direct marketing' as the communication (by whatever means) of any advertising or marketing material which is directed to particular individuals. In other words, if you would add your phone number to the standard Data Protection Notice they should leave you only (after a 28-day period).

It's worth noting you don't have to send a formal letter to stop unsolicited phone calls. You can simply send British Gas an informal e-mail asking them not to "market" you by phone. You would still need to allow them up to 28 days to comply with your request. If you sent your e-mail more then 28 days ago you should consider making a complaint to the Information Commissioner's Office.

It's worth noting that the rules for unsolicited phone calls are much stricter than the rules for unsolicited mail. The Mailing Preference Service, for instance, is merely a voluntary industry scheme. There's no legal obligation for companies to check if people on a junk mail database have registered with the Mailing Preference Service. Companies that are members of the Direct Marketing Association are expected to check the Mailing Preference Service 'suppression file', but there's no legal obligation for them to do so. However, any company that wants to make sales calls is legally obliged to check if any telephone numbers on a marketing database are registered with the Telephone Preference Service.

In short, the answer to your question is 'yes'.