
You need to refund your buyer and then claim from Royal Mail for the loss....if you have proof of posting (doesn't have to be recorded delivery) you will be covered for up to about £32. If you don't have proof of postage then I'm afraid you're not entitled to anything back from Royal Mail. I'm not aware of any means of claiming through Paypal either.
Of course, there is always the chance that the buyer is pulling a fast one...has seen that you didn't send by trackable means and is saying that that haven't received it knowing that you will have to refund. Unfortunately, this sort of thing happens a lot and even more so now that sellers can't leave negative feedback for buyers...even when the buyer turns out to be a complete con artist!