My horse had the same problem, I just bought a saddle by Kruger saddlery, they are based in Pontefract, which may be within reach depending on where in the North West you are.
She will bring a selection of trees out and fit the actual tree to your horse, then build the saddle and fit it at your yard.
Mine is in lovely calfskin, and would be around £1,600 new.
Some of the Strada trees are flat which is why I ended up with one. Really nice to ride in. Have heard good things about AH saddles too but no personal experience.
Having two very, very flat profiled horses they are in the Equipe Olympia and Kent and Master original. Also being NW based I would not hesitate to recommend Freedom Saddlery, Steph is a miracle worker!