I have started issuing data protection notices to senders of unsolicited catalogues and, in the main, this is working. However one offender, Pia Jewellery, has replied that we are not on their database because the catalogue comes from a "third party". They have, in fairness, added a note that if, when the next catalogue arrives, they may be able to tell me who is sending the catalogue if I provide them with certain information. That seems a huge cop out to me. Can I complain to anyone about this type of behaviour?
From what they've told you it appears that when you request a catalogue via the Pia Jewellery website (using an unencrypted connection!) the information is automatically submitted to a third party. In that case it might be true that your personal details don't appear on Pia Jewellery's database. However, the data would appear on the database of a third party that is acting on Pia Jewellery's behalf.
From a data protection perspective this position is complicated. Perhaps the best way forward is to ask them politely to give you the name and contact details of the third party that is processing your personal data on Pia Jewellery's behalf. If they refuse you could give the Information Commissioner's Office a call on 01625 545 745 – they should be able to clarify whether or not Pia Jewellery is, legally speaking, processing your personal data. The Information Commissioner's Office is the body enforcing the Data Protection Act and its help line is very friendly. They're also the body you could complain to should the issue not be resolved.
As an aside, I suspect the mysterious third party is sending junk mail on behalf of lots of companies. Finding out who they are might stop quite a few other catalogues as well.