Green’s Dictionary of Slang

1. to gather rags for a living.

1861		(con. 1840s–50s) H. Mayhew London Labour and London Poor I 417/1: He goes tatting and billy-hunting in the country (gathering rags and buying old metal).
1958		D. Reeve Smoke in the Lanes 145: You’d jest so well pick up wot you wants offen the ole rag-trolley after you’ve bein out a-tattin. [Ibid.] 173: ‘Tatting’ is a gloomy business.

2. (US gay) to piece together, to create something out of left-over bits and pieces.

1972

B. Rodgers Queens’ Vernacular 194: tat up (Brit gay sl) to piece something together; to create something new out of leftovers.