One2go,
First of all, I'd be quite surprised if your ATPL gives you SE privileges in the way you'd imagine. In order to fly a SE aeroplane, you must have a valid license (your ATPL will do just fine for that), and you must also have a valid Single Engine Piston class rating. I doubt if your class rating is valid - the normal way of keeping it valid would be to fly 12 hours of SE in the last 12 months of each 24 month period. It must be SE time - ME time doesn't count - which is why my guess would be that yours has expired.
Assuming that your SE class rating has expired by more than 5 years, you must take a test (basically the same as PPL skills test but without the navigation part) with an examiner, and send some paperwork in to the CAA along with a fee. Only the CAA can renew your rating if it has expired by more than 5 years. For less than 5 years, the examiner can renew the license but you still need to send some paperwork off to the CAA. You might decide that you need a few hours of instruction before this test to bring you up to standard.
Once you've got that sorted out, get yourself down to your local flying club where you should be able to hire an aircraft after being checked out by the club's instructors. Or else buy your own aircraft, or a share in an aircraft.
You specifically mention CofA versus PFA. Not quite sure exactly what you're looking for..... an aeroplane is an aeroplane, whatever type of certificate it's got. The biggest difference is in who is allowed to maintain the aircraft (you must be a licensed engineer to maintain a CofA aircraft, apart from a short list of small items that an owner can do himself). Also, PFA aircraft are day VFR only, and not allowed over built-up areas. If there's anything else more specific that you want to know, then just ask.
Hope that's at least a start for you!
FFF
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