Sorry if I'm repeating myself, but that's between you/me and Virgin Media.
A third party is not privy to the contract, there's a doctrine in contract law, 'privity' of contract which means 3rd parties cannot be binded by contractual obligations or benefit from them. I know there was a Contract Rights of Third Parties Act but that won't affect this situation. VM's contract has 0 to do with legal liabilities for you, it only saves their asses if you get sued.
It's been ages since I've opened a contract law text book, was like 5 years ago now. A couple years ago I am pretty sure I remember reading a case about an internet cafe that gave the option for burning downloaded files onto CD, that was very relevant to all this. So if anyone wants to look that up... Again I think the common carrier provision may apply to leaving a wireless network open, because you are, de facto, a service provider.
Check this post out
I wrote something at uni about cliaments not being able to prove P2P file sharing causation as it won't satisfy the balance of probabitlies test, much like asbestos poisoning since P2P is a chunk based system, unlike FTP. Since each defendent only harmed the D partially, you cannot satisfy the test of causation which requires >50% ('all or nothing', 'winner takes all' it's called) unless courts invent law to support your case. I can see the justice in people dying of black lung in making up laws, but not in copyright infringement lol
And it's a joke to say you're gulity in a civil case, as a poster above said it's a balance of probabilities test. In most cases if you don't have many assets it is worth taking any company to court. Firstly they will be worried they wont cover costs, since if you have no assets they have nothing to take.
And also it doesn't take years of training to understand a narrow area of the law, infact it takes maybe a couple months. So you can become an expert in a short period of time, so its worth knowing your rights, researching and engaging in a legal argument with the people trying to sue you. They will try and drown you in legal jargon but in reality the only thing they normally have is a ton of muscle (money) and little else.