Green’s Dictionary of Slang

the Royal Naval Volunteer Reserve; also as adj.

1916		Hull Dly Mail 22 Sept. 2/4: Officers and men of the Patrol Service [...] have two distinct titles for it. The officers call it the ‘Wavy Navy’ [...] and the men term it ‘Harry Tates’s Navy’ because there are hundreds of comedians in it.
1918		W. Owen letter 21 Mar. Coll. Letters (1988) 541: Her son, a Lieut. in the ‘Wavy Navy’ was at home.
1931		Exeter & Plymouth Gaz. 25 Apr. 5/6: He said its members had been variously described as the ‘Wavy Navy’ and ‘Harry Tate’s Navy’.
1939		Hully Dly Mail 13 Nov. 4/4: The Admiralty has called upon considerable numbers of these men for the ‘Wavy Navy’.
1944		A. Jacob Traveller’s War 40: The ship’s doctor and the paymaster-lieutenant, both ‘Wavy Navy’ men [...] have been in the service only a few months and know next to nothing of the sea.
1950		Dundee Courier 3 June 3/1: Wavy Navy in Action [...] Ex-servicemen whose complaint was that the wavy navy never received the limelight it merited.
1960		D. Fearon Murder-on-Thames 115: I remember him when he was a Sub. He was Wavy Navy then.