Are you looking to block individual numbers or marketing calls? If you are looking to block individual numbers then we don't have a call feature that will facilitate this, there is an Incoming Barring feature but this only bars all calls. The best thing for this is to purchase a handset/device that allows you to control what calls are allowed through and which are not.
If it relates to marketing calls, the above can help as well but we do have a feature called Anonymous Caller Reject that can help with this providing they are UK incoming calls.
Caller Display (If you don't already have it) will allow you to see who is calling and this can be a handy feature in combating unwanted calls.
All our call features available can be found here: Calling Features. If you wish to add any of these features, just give our team a call on 150 Free from your Virgin Landline or if you prefer to chat online you can do so via our Contact Us page.
Let me know how you get on, we're here to help.
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Thanks for your comprehensive answer! I now realise that the answer to what I'm looking for lies in the phones themselves, rather than with the service provider. I need to buy myself a phone with the appropriate feature built-in.