The wireless adaptor suggested by Aragorn is a possibility but may be a fiddle to set up. As you will potentiall have three different devices in your house, your computer, Wii and the new laptop, it makes sense to do this properly. Get a wireless router. They aren't especially expensive, and can be set up fairly simply. Best advantage is if you just want to use the Wii, or the laptop, your computer would not have to be on. You'd be able to use the inbuilt wireless adaptor on your Wii too, ditching that USB dongle.
Virgin Media will supply a router, or alternatively they can be bought from any decent computer store. You need to ensure it is compatible with cable (no integral ADSL modem), but for your needs i suspect you only need "g" standard wireless.
Not a recommendation for PC world but something like:
http://www.pcworld.co.uk/martprd/sto...&category_oid= or
http://www.pcworld.co.uk/martprd/sto...&category_oid= should do the job.