The 75p is for your First Class Large letter stamp, folly, the extra 77p is for the signature upon arrival, so the recipient can't claim they haven't received it (for your records). It's still a First Class letter, so it SHOULD arrive within 1-2 days.
The reference number you've got on your receipt isn't a 'tracking' number, it's your proof of postage reference to find the signature online. The only way to guarantee a day of arrival and to get an ACTUAL tracking number is to use Special Delivery. Quite a price difference, but a big difference in benefits, too.
Recorded Signed For mail data isn't automatically updated online as Special Delivery is, so it doesn't mean that it hasn't actually got there yet. Give the number on your receipt a call with your reference number if you're worried, though. :)