Right no DNS, then try IP addresses instead. DNS is the conversion of internet 'names' to IP addresses. Use an IP you do not need DNS.
With router plugged in, all cables checked open cmd and type
tracert 212.58.224.115
that is the IP address for bbc.co.uk. If that works type in your address bar:
http://212.58.224.115
You should reach the BBC through your browser
then you know it is DNS.
Did they get you to check that, if DNS not working no way would ping
www.bbc.co.uk have worked, as a DNS request from your system would not have been received so therefore your system would not have been able to resolve the name>IP address. Now you have the correct DNS IP addresses for your local network (Virgin one) set up everything will be fine - the IP>>name requests will be replied to