Are you using a "Cable/DSL" router in conjunction with Virgin Media's *CABLE* service?
I have several Cable/DSL routers of different makes and with each one, if I've run the Setup Wizard, the final check at the end to see if there is an internet connection has failed. Despite this, they have connected perfectly. If this is your problem, close the wizard and check if the router is actually working.
When swapping over the connection to the Cable Modem from the PC to the Router, the Cable Modem must be powered off and left without power for three or four minutes, so that it loses the association between the existing connection and the IP address it has allocated to it. It will then recognise a new connection and allocate a different IP address to it.