The CAA have a charter which requires that they turn round your licnec application within 10 working days of receiving your paperwork. So as soon as it hits the licence production teams' in-tray, assuming that all your paperwork is error-free you should expect to receive your licence about a fortnight after sending your application off.
You did send it by Recorded Delivery, didn't you?? If so, use
www.royalmail.com track and trace to check when your paperwork was delivered. If in doubt, pay another £2.20 and ask for Proof of Delivery; the Royal Mail will then send you a copy of the signature of the actual person who signed for your paperwork at the Belgrano.....