Yup - seconded; whether I'm looking to seel something either on here or eBay, I always insist that it gets sent via Recorded Delivery.
Sadly, your buyer isn't responsible if the Royal Mail screw up....although the liability isn't technically yours either, you have his money and he has...well...nothing!
Unless you can reach a compromise of some kind, I'd advise you to reimburse your buyer (give it a week or so first, to see if it's merely been delayed, rather than lost completely).
Not doing so is likely to lead to two issues cropping-up:
1) Your buyer will possibly post on here, amking everyone aware of what's happened
2) Your buyer (if he paid with PayPal), may well file a complaint, which will lead to them either recovering the monies from your account or freezing your account.
Neither option is a good position to be in...sometimes, it's just best to learn from the experience, and accept that you're going to be out of pocket this time
Rob