Green’s Dictionary of Slang

describing a person’s hair, e.g. well-thatched, having a good growth of hair.

1873		Sl. Dict. 320: ‘He’s well thatched,’ is said of a man with a good head of hair.
1887		‘’Arry on Angling’ in Punch 30 July 45/1: Jack’s a straw-thatched young joker in gig-lamps.
1905		‘Doss Chiderdoss’ ‘What Winifred Wanted’ The Sporting Times 29 Apr. 1/3: Her ginger-thatched hubby had brought her a lot.
1908		Sun. Times (Perth) 13 Sept. 4/8: The long-thatched Kooby was enquiring [etc.].
1956		‘Toney Betts’ Across the Board 251: A burly, white-thatched Kentuckian.