Read this thread start to finish, including the linked posts I've replied with.
The whole "Free TV" marketing episode strikes me as a poorly conceived idea by Virgin Media, and whilst it did what the company wanted (brought in new customers), the company have got cold feet and don't want to fulfil their side of the offer. The law is on your side, that if you rely on marketing material when entering a contract, those marketing promises are legally binding. But if VM won't readily comply, you will need to raise a formal complaint with the company, and if (when!) they still don't offer a TV or equivalent cash, you would need to escalate to the free arbitration service. If the company resist, then this process will not be quick and you'll have to put in some work writing out the complaint (background, the offer, your decision to join VM etc), but possibly that's the price of the free TV.
You could use the small claims process of the county court (which is now all online), but the courts take a dim view if you haven't tried the company's complaints process and then arbitration, added to which you'd need to invest time speaking to people like Trading Standards and Citizens Advice Bureau before trying a solo small claim against VM.