Unless you have proof of delivery, if the buyer has opened a case through Ebay, you should refund them.
Your claim against Royal Mail will cover the cost of the item (as long as the cover was sufficient - Signed For only covers up to £20 - and the item was one covered by the service you used) and the postage cost you paid.
"There are two ways to be fooled. One is to believe what isn't true; the other is to refuse to believe what is true.”
Søren Kierkegaard, Danish philosopher (1813 - 1855)