As has been previously been mentioned a simple flight around the outskirts of the UK would not take long in a powered light aircraft and would not be more challenging than managing fuel/radio (navigation is done by following the coast in general).
What would be challenging would be to do it in a glider, but for powered aircraft another challenge would be to do the round the coast challenge landing at each and every aerodrome within X distance of the coast getting verification from the tower at each aerodrome and proceeding to the next - this could be mixed with pilots alternating each of the legs of the flight.
There are of course a number of considerations to account for....
1) Aircraft and aerodrome - not all aircraft are suitable to land at all aerodromes.
2) Sponsorship - flying for reward may/may not require specific licence requirements from the CAA (e.g. cpl).
3) Landing fees - I would imagine some aerodromes would waive these for a charitable flight made known in advance.
4) Cost - Bearing in mind if you took as little as only £50 an hour for fuel whilst in the air, 1 hour a day for 12 days is £600. You also have to factor in staying somewhere each night of the 12 days.
5) Insurance - Will your standard insurance cover you for a trip such as this.
6) Alot of GA aerodromes require prior permission to land - this would involve a large admin task to obtain prior to such an event.
7) Any entry fee has to take into account the costs of actually participating.
8) Weather - you cannot rely on weather, most GA pilots are restricted to VFR and will not be able to fly if there is a low cloud base, rain etc etc
Some of the above probably can be answered quite quickly by those on here - I am not far enough into my ppl to do so. I hope to gain my ppl in January and would definately consider doing this if practical.