so I can terminate the contract without any penalty, right?
Don’t worry about it, there is NO contract, VM can’t supply a service and you haven’t agreed to pay anything.
I have an existing contract at my current home with a few months left.
I think I have to pay the early disconnection fee and get a refund later. I would like to know the detail procedure and what is considered as "valid evidence of the new address"
If Virgin Media isn't available at your new address, you’ll need to cancel your Virgin Media service. Unfortunately, if you’re still in your minimum term, this means you might have to pay an early disconnection fee for ending your contract early. If you're moving outside our network area but still within the UK and you give us some valid evidence of your new address within 30 days, we'll credit you back the early disconnection fee. Our team will let you know the full process, so you'll only pay what you need to.