I'm very bored at the moment:
At 2000' you would get a max theoretical receive/xmit distance with VHF of 56nm, 69nm at 3000' and 97nm at 6000' (1.25*SQRT(height')). Explains why there will probably be holes in the coverage with only 9 transmitters in the UK. If you loose contact climbing might work.
Assuming the UK is square: If the UK is 115,000 sq nm then SQRT(115,000/9) = 130nm. Knowing that the UK isn't square then some transmitters will be closer and some further so assuming that max distance between transmitters is 130 * 1.5 = 195 then with this ludicrous guestimation/approximation you would have to fly at 24,000' to ensure constant coverage (195 = 1.25*SQRT(x) = 24000)) throughout the UK.
OK, I know it is a worthless calculation but that's 10 minutes less time to fill
