Why the Treasury would not define a heavy cruiser

What stops the Treasury from forcing the Royal Navy to define a heavy cruiser for financial reasons?

Classification is outside its normal remit; the Treasury controls money, while cross-department terminology is a Cabinet or prime ministerial matter.

Financial power lets the Treasury approve, constrain, or reject a ship program without deciding what the Navy calls the result. Classification remains part of the service and departmental framework in which the ship's mission is defined. Imposing terminology across departments would intrude on coordination belonging to the Cabinet Office or prime minister. The Treasury is especially unlikely to force that confrontation because the prime minister can replace the chancellor and reset its political direction.