Green’s Dictionary of Slang

unsteadily; thus as n., an old and unsteady person.

1847–81		Halliwell Dict. Archaic and Provincial Words II 930/1: Wibble-wobble Unsteadily.
1880		Reynolds Newspaper 12 Dec. 2/5: A peck of jewels will often do a good deal towards convincing a wibbly-wobbly Republican.
1888		Pall Mall Gaz. 1 June 4/1: The less informed are Free Traders, the Conservative leaders are wibble-wobble.
1890–1904		Farmer & Henley Sl. and Its Analogues VII 349/2: Wibble-wobble [...] Unsteadily.
1893		Manchester Courier 21 Jan. 9/1: Now it is a crinoline panic; though there would be no ‘only’ about it if the invasion of the hated ‘wibbly-wobbly’ cage were really imminent.
1896		Cornishman 14 May 3/1: The two newest crazes are bicycling [...] We cannot all ride on the wibble-wobble saddle.
1902		N. Devon Jrnl 23 Oct. 7/1: ‘How can you tell [...] when Satan is speaking to you?’ [...] ‘When you hear a wibbly-wobbly noise in your inside’.
1913		Derby Dly Teleg. 30 Sept. 2/7: ‘The wibbly-wobbly walk’ speaks for itself.
1919		Western Dly Press 4 Dec. 6/3: Now once again the wibble-wobble policy is being re-introduced by those who seemingly know not anything of agriculture.
1922		Joyce Ulysses 387: Drat the man! Bless me, I’m all of a wibblywobbly.
1988		A. Hollinghurst Swimming-Pool Library (1998) 36: When you get to be an old wibbly-wobbly, as one, alas, now is.