IIRC, it's because the British Army can trace its origins back to the New Model Army, so pledging allegiance to the Crown was more than just a formality back th

IIRC, it's because the British Army can trace its origins back to the New Model Army, so pledging allegiance to the Crown was more than just a formality back then. In contrast, the 'Royal' Navy was created expressly by the monarch so allegiance is implied.