Call into 150 (from a VM phone) or 0345 454 1111 (from any other line) -> enter the main menu -> option 2 (faults) -> report a TV fault. Yes the remote is part of your TV service so this is the option to use. If asks to run a automatic service test before putting you through to an agent. Either let it, or go with a skip test option if given the opportunity. Once through to an agent, ask for a replacement remote.
Alternately, you can ask for a replace via the web chat: http://www.virginmedia.com/contact/ -> TV -> help with my remote control -> Chat Online. Access this page from a desktop or laptop. Do so between 9AM to 5PM. If it says all agents are busy, reload the page every three minutes and check again.
- - - - - - Any opinions expressed by myself are entirely my own and do not represent Virgin Media in any way.