Go here and have a good look at this site.
It contains the following among other things.
"YOUR RIGHTS KNOW YOUR CONSUMER RIGHTS WHEN BUYING GOODS IN THE U.K.,
and GETTING SATISFACTION WHEN THEY GO FAULTY.
Read how some High Street dealers try to deprive you of your rights."
"From Spring 2003 improved regulations came into force which ADD to those discussed below. It is understood these allow you to return goods as FAULTY SINCE MANUFACTURE within six months. If you feel this applies to you please check first with your Trading Standards Officer."
Forget where the computer was made your claim is with PC World.
From what you have said you should have no problems, but check with your local trading standards office first.