Interesting idea . . . BUT . . . I can't see the Navy giving up any of it's assets and missions, at least without a hell of a struggle, particularly those that it would consider 'traditional', such as the defence of Naval Bases, which presume in this scenario, would pass to the new Defence Force.
The thing with the OTL formation of the RAF, was that both 'sides', the Army and the Navy, both 'lost', with both their air assets being passed to the newly formed RAF. In addition, for both forces, the air capability was new, and thus hadn't really had time to become fully bedded in to either service's traditions.
On the other hand, for the Navy to not only give up assets and missions, including ships, but to give them to the Army, would be too much for Their Lordships to stomach . . .
cheers,
Robin.