The first thing is to check PPR requirements, mandatory handling, etc. So get the details from Pooleys and give them a call.
The only UK airports you actually cannot fly to are Heathrow and London City. The others are all OK to go to but some cost silly money (e.g. Gatwick is about £500 including the handling cost, and 24hrs PPR).
Having got that sorted, it is just a case of flying there.... Get the ATIS in good time, and call up their Approach frequency telling them you are "inbound" and whether VFR or IFR - the usual position report. They will tell you what to do. Normally you get transferred to the Tower frequency when somewhere near established on final approach, so have that set up on the radio too.
The bigger ones also have a Ground frequency, and again Tower will tell you if/when to switch over to it. However, even if the Ground frequency is published it often isn't in use so you stay on Tower until shutdown.
When departing:
The bigger airports often like to do a clearance to start the engine, so call up Ground with "Gxxxx request start". Then call up either Ground or Tower (I can never remember which but Ground is a good bet) for a departure clearance (yes, even for VFR - the d.c. will be brief e.g. "after departure climb 600ft then turn right to Hengisbury Head, not above 2000ft").
It's really very simple.
I think it's fair to say that many pilots get lost at every bigger (or smaller
) airport they go to. I certainly do. So have the airport map to hand. Before calling up for departure, locate yourself on that map and work out the taxiways so when you acknowledge the first taxi clearance, you kind of know what they are talking about
The fact that the airport is in CAS is really not relevant. You will be issued with a clearance to enter the CAS on your way in - they can hardly not do that if you are inbound!
I fly around Europe a significant amount, and the biggest hassle is PPR and silly costs. In many places abroad you have separate PPRs for a landing, avgas, Customs, and each of these has to be sorted with separate phone calls, faxes, etc. The UK should be easy in comparison.
Some airports are PNR (prior notice required) but this is de facto same as PPR because you have to be sure they got the notice, so you still need to contact them anyway.....
Some of this stuff can be solved (or circumvented) by telling ATC you are vistiting the local aeroclub there. Obviously, it is desirable to square this up with the aeroclub first
Upmarket GA pilots just call up the handling agent who (for a fee) sorts out the nonsense.
Flying is the easy bit. It is all the crap on the ground