I think that is the case where the letter might have gone missing. However, as I understand it, you are not claiming it has gone missing ... it was delivered successfully ... but merely the Post Office neglected to get a signature before they handed it over.I think that I'll wait for my docs to be returned until I start in with the post office. You have to wait 10 working days anyway apparently.
So I think, make it clear that the letter has not got lost, it has been delivered, and ask for the return of the Special Delivery fee that you paid.
Last time I had cause to do this, a letter posted to Companies House, sent Recorded Delivery, delivered but not signed for, I ended up getting a couple of books of stamps, worth far more than the fee I had paid.
Presumably the Track & Trace is not yet indicating a delivery date/time?