Section 11 of the DPA states that a data subject (that's you) has the right to require a data controller (that's the junk mailer) to stop processing his or her personal details for 'direct marketing' purposes. The Act doesn't specify exactly how a data controller should comply with such requests – it just tells them to comply.

It seems that the company you've been dealing with might benefit from the Information Commissioner's guidance. Simply removing your personal details from their junk mail list and then adding your details again (when they buy a new junk mail list) would be a clear breach of the Data Protection Act. They have to make sure, one way or the other, that they don't use your personal details for 'direct marketing'.

In short, the Act doesn't in any way oblige junk mailers who you've sent a section 11 notice to remove your details from a junk mail list – it only obliges them not to send you any more junk mail. And although the Act doesn't tell senders how they should make sure that they'll leave you alone it would probably make sense for them to put your name and address on a 'do not mail' list.

As an aside, when companies buy a second hand junk mail list they should make sure that nobody on the list is registered with the Mailing Preference Service. I'm not too sure many senders do this but, at least in theory, registering with the opt-out scheme should prevent your name and address are sold by list brokers. There are loopholes though – by hiding opt-out boxes junk mailers often get your consent to do with your personal details as they see fit. (But of course, sending them a data protection notice will force them to stop using your personal details for 'direct marketing' purposes).