If you go on to a well known internet auction site and type in the name of the aeroplane you had in mind, followed by "wood", you will find various companies in the Far East or Eastern Europe who will carve and paint you one. Find one with plenty of good feedback and who will send you photo updates of its progress. Judging by the ones I looked at the quality is very good.
There are no doubt people in the UK who will do this as well, but don't expect it to be cheap.
If you are designing your own colour scheme, it would be worth getting some paint samples e.g. Humbrol, of the colours you had in mind, as with a unique scheme you are leaving it to the painter's interpretation. Buying and posting over a BS4800 or RAL paint chart would be another way.