I don't think you simply have to accept you've lost here.
The sale of goods act states that there is no legal requirement to provide a receipt on a sale, which means that there is NO requirement to keep, or produce a receipt. You paid for a service that the Royal Mail have clearly failed to provide. If the Post Office counter staff remember you and can vouch for you, or if you paid by card and can produce a bank statement you might have a case.
I'm unsure if your statutory rights cover things like mail, but it's worth checking out. At the very least, a claim with a threat of small claims action may be worth pursuing. They might take the view it's a relatively small amount and even winning at small claims will cost them more than that.