I sympathise with your health problems, but with respect they aren't relevant to your dispute with PC World.
That all boils down to a simple issue - that you claim the company isn't meeting its obligations under the terms of the Premium Cover policy you paid for. It's difficult for any of us to comment without having details of the cover you paid for.
If you are referring to the 'Whatever Happens' Premier cover, the terms state that If PCW can’t fix your problem within 7 days, you can request a replacement product to the equivalent specification. You are also guaranteed a 'next day' courier collection if you aren't taking the laptop to the store.
You state that neither of these terms were complied with, and if that's correct, PCW was in breach of its contract with you. You say that you were told the laptop had been written off, but that PCW has failed to supply a voucher for a new machine. The company has cancelled the voucher because it suspects a fraudulent claim.
If that's a reasonable description of the circumstances my opinion is that you wait for a reaction to the letter you have sent, and let us know what response the company makes.