The Data Protection Act states that (UK-based) organisations have to remove your personal details from its mailing list if you ask them to do so. The body that enforces the Act, the Information Commissioner's Office, recommends that you make such a request by sending a so-called data protection notice. Ignoring such notices is a breach of the Act, so should Afibel's junk mail offensive continue after you sent them a notice you could next lodge a complaint with the Information Commissioner. Ultimately, you could take them to court if they don't stop – but I'm pretty sure sending a notice will do the trick.

Afibel's privacy policy explains that they're dead-keen on offering its customers the chance to sign up to third party email marketing. If you've done business with Afibel in the past I'd ask them in the data protection notice whether or not they've passed your personal details to any third parties, and if so to confirm the names and contact details of those third parties – you could then send those third parties a notice as well. Afibel's privacy policy states that you can send your request to sales@afibel.co.uk:

If for any reason you are concerned that the personal information maintained by the website is not correct, or should you wish to have your name removed from our records, please contact us at service@afibel.co.uk and we will be happy to review, update or remove information as appropriate. We will always let you have a copy of all information we have on you should you request it.

Finally, as an aside, your registration with the Mailing Preference Service is unlikely to stop junk mail from companies you've done business with in the past.