Virgin Media sends three types of unsolicited mail: addressed, unaddressed, and 'To the Occupier' junk mail. All need a different approach…

• Stopping personally addressed junk mail is fairly straightforward; you'd need to send Virgin a so-called 'data protection notice'. More information and an example letter / e-mail can be found in the Guide to stamping out junk mail.
• For the unaddressed junk mail Virgin Media hires Royal Mail. To stop all leaflets delivered by the postman you can sign up to Royal Mail's Door-to-Door Opt-Out. Be aware you may need to remind Royal Mail of your registration a couple of times before they stop delivering leaflets to your address.
• Finally, junk mail addressed 'To the Occupier' is difficult, if not impossible to stop. If the junk mail doesn't include your address (like so) it will be prevented by the above-mentioned Door-to-Door Opt-Out. But if an item does include your address you're buggered. A while ago I written about How to stop 'To the Occupier' junk mail from Virgin Media on my blog. (Also read the comments from other people trying to stop this particularly annoying type of junk mail.)