Entry from OED Online

wally, n.² (and a.³)

SECOND EDITION 1989

[Origin uncertain: perh. the same word as WOLLY. Said by some to be the dim. of the personal name Walter: cf. CHARLEY, CHARLIE 6. Cf. also WALLYDRAG, WALLYDRAIGLE.]

An unfashionable person; one who is foolish, inept, or ineffectual. Also as a mild term of abuse. Also attrib. or as adj.

1969 Daily Mirror 10 Oct. 19/1 Wally, out of fashion. 1974 Times 8 Aug. 2/4 The successors to the flat-earthers..are at present encamped on the perimeter of the great concentric stone circles... They choose to be known as the Wallies of Wessex, Wally being a conveniently anonymous umbrella for vulnerable individuals. 1976 Telegraph (Brisbane) 8 Oct. 10/4 The Arnolds call anybody who wears conventional clothes, such as jeans or skirts, a Wally. 1979 Listener 20 & 27 Dec. 861/1 Cuban heel boots..are..like a Wally uniform... John Travolta, the Bee-Gees and Boney M are considered Wally acts. 1983 Evening Star (Ipswich) 20 June 7/1 He shrugged off Ms. Ford's throw as temperamental but I bet he felt a right wally. 1983 P. INCHBALD Short Break in Venice xviii. 177 Keith cracked a joke over the radio and got called a bleeding wally. 1984 Daily Tel. 14 June 1/4 ‘They looked a right load of wallies,’ said an eye-witness. 1985 M. STOTT Before I Go iv. 77, I shall seem more of a ‘wally’ to them than ever because I don't know half the leading telly presenters.