Green’s Dictionary of Slang

tommy n.3

[Gk tomé, a section; orig. Trinity College, Dublin]

a worn-out shirt.

[Ire]Tipperary Free Press 29 June 2/6: He was dressed [in] a pair of nondescript unmentionables and a calico breast-plate vulgarly y’clept a tommy.
[UK]Hotten Dict. of Modern Sl. etc. 238: Tommy ― See DICKEY [i.e. ‘a worn out shirt, but means, now-a-days, a front or half-shirt’].
[UK]Sl. Dict.