Taking a slightly wider view of where one can and cannot land (there is a world outside the UK too):
If you file a flight plan which gets accepted, and you get notams, and the notams don't show up any special requirements, and you have checked the airfield opening hours in the relevant AIP, then you can fly. This is what most people do.
In the past, I have tried to be extra diligent and faxed airports for any details I needed to know e.g. avgas. Venice once replied that it is closed to GA. This is rubbish - had I filed an IFR flight plan there (it is 24H etc) I could have just gone and they would not have had any choice but to accept the flight.
Corfu LGKR plays a similar game. The notams used to show something like 24HR notification (nothing at all in today's notams) but if you ask them they will say it's 5 days, to "regulate apron capacity"! The GA apron big enough to land on and rarely has more than a couple of rusting spamcans sitting in the far corner.
Take Cranfield. If you call them up saying you would like to land with an ILS, they will probably say they can't accept you due to training activity. But if you file an IFR flight plan, and it's accepted, and the notams don't contain any special requirements (they certainly don't today; just checked) then they have to accept the incoming flight. They just don't like "UK bimblers" arriving and asking for an ILS - despite charging them some £50 for the privilege.
So sometimes it pays to play it purely by the rules, file and fly. It's a shame because phoning the airfield beforehand should always be a good thing to do, and checking fuel availability is pretty essential in the further away places.
Duxford is weird. I was on a flight once where they refused a landing due to no PPR. Calling them from the aircraft on a mobile phone was apparently not acceptable either - they said if we land at Cambridge that will be OK. I can see that PPR is the result of planning restrictions but it is often a complete joke, since one can make a phone call from an aircraft if low enough especially with an adapter like the Safety Cell thingy.