I was answering wudys last 7 words, which I agree, having re read the question was slightly confusing... what I should have said was
yes you do have to buy a router.
though as LeMarchand says there is another way to do it, but it's will work out about the same cost and is considerably less practicable as you would need to have your desktop turned on when ever you wanted to use your laptop.
Also as correctly pointed out the link I posted is for a router that's used with broadband via a telephone line, if you have a cable connection with virgin then that would not be suitable.