I had heard a rumour that any CP licence issued would roll over after its three year expiration date, but that does not seem to be the case (see above link).
If you already hold a valid qualification the three day refresher to get the licence is pretty run of the mill and several security companies run these courses. You need your First Aid at Work ticket first though.
Thanks for that, Afghanman.
Yes, it would seem that you don't actually need to do any "additional training" for this renewal (apart from the normal first aid qualification). So just a paper exercise then and, of course, payment.