A recorded delivery is not guaranteed to arrive in any way over and above the standard postage, they go in with the rest of the mail and the only difference is that a signature is required upon delivery.
Has your recorded delivery actually been confirmed by the recipient as not having arrived? As I can almost guarantee it has been delivered, it just wont have been confirmed into the system due to one of several reasons - postie could be off sick/on holiday/failed to hand in the delivery card for scanning, person in the locker might have had the card back but hasn't scanned the barcode or has missed it, website hasn't received the conformation, etc etc.
It happens a lot, recorded deliveries actually going missing happens very very rarely - less than 1 in 50,000. Another thing to remember, you sent the letter, you have conformation it was sent, so stick to your timetable.Do you think the bank would listen if they said they'd sent you a letter and you said you'd never received it? Of course not.
Royal Mail recorded delivery is not a reliable service. It would be extremely interesting to see statistics from Royal Mail as to what percentage of recorded delivery items are actually signed for. In my experience it is extremely unusual to be asked to sign for a recorded delivery item. Indeed, I received one yesterday where someone (probably the postman) had removed the recorded lable before delivering it without obtaining a signature. Additionally many items are prohibited from being sent by recorded delivery