As it is a "network printer" with an ethernet port, the simplest solution would be to plug it into the Virgin wireless router in Room 2. Any computer connecting to the router, whether by ethernet cable or "wirelessly", could then print from it.
Wireless routers incorporate a Wireless Access Point to which Wireless Network Adapters (in computers) connect, but two Wireless Access Points (routers) cannot communicate directly. If the printer has to be in Room 1 and connect wirelessly to the router in Room 2, then you would need to install a Wireless Network Bridge.
A Wireless Network Bridge is effectively the opposite of a Wireless Access Point:
Wireless Access Point - allows wireless devices to connect to a wired network.
Wireless Network Bridge - allows wired devices to connect to a wireless network.
...if I haven't made that too confusing!