My PC broke down yesterday and I rang PC World who will send an engineer around a week today (2nd May). It is still under extended insurance so it should still be free, because far as I know I haven't done anything. Do you think I am right that this should be free?
Well, without knowning exactly what's been covered under the extended warranty, it's hard to say. What you think should be covered may very well not be, so you may want to dig the warranty info out and look over it to see if any stipulations apply.
Yes it depends on the exact warranty details. Usually with PC World, as long as you haven't tampered with it, and it is a component failure then they will usually repair it.