Quote:
"All claims must supply as a minimum the following “basic evidence”
the names and addresses of the sender, addressee and claimant,
the Royal Mail product used,
the postage paid and method of postage e.g. stamps, franking impression
the place of posting,
the date of posting,
the basis for asserting the posting details and product used (such as date of postmark, certificate of posting (if available) and for Royal Mail Special Delivery Guaranteed by 1pm® and Royal Mail Signed for® the product documentation and
a description of the contents."
Source:
https://www.royalmail.com/retail-compensation-policy-loss
It's the "the basis for asserting the posting details and product used" that might present you with difficulties. Even if you can persuade Royal Mail to cough up, their liability is limited to six first class stamps (or the actual postage paid, if higher).