we have two computers on our network. We are also with virgin (ntl) and the IP address is based on the modem not the computers iyswim.
So if you have two computers on the same network they will both have the same IP address (which is why it's so essential for your network to be secure as someone could download illegal material through your network for instance and it would show up as your IP address and would be traceable to you).
There should never be two computers with the same IP address on your network. You probably want to make sure that they are each set to obtain an IP address automatically, like this: http://uits.iu.edu/page/aiyy
Checking that your WiFi is secure is a good idea too.
Some of the answers here are wrong. You should not have two computers on your local network (LAN) with the same IP address.
Your LAN address will probably be something like 192.168.0.2 or 192.168.1.2, and each computer can either have this fixed in their network software configuration (which it sounds like you have - both computers have the same fixed address) or they can get their address from a service in your router called DHCP - you need to set your computers to use DHCP.
All computers on your LAN will appear to the outside world to have the same IP address though, which may change from time to time but is unique to your LAN in the whole world.
If you check your computers and they all have different addresses and you are still getting this message, it is likely that someone is gatecrashing your network and evesdropping on your communications.