Green’s Dictionary of Slang

titley n.

[? dial. titley tickle; i.e. one’s palate or SE tiddly, small, i.e. a small portion; var. on tiddly n.]

a drink.

[UK]Hotten Dict. of Modern Sl. etc.
[UK]Sl. Dict.
[UK]‘William Juniper’ True Drunkard’s Delight.
[UK]Partridge DSUE (1984) 1240: [...] C.20.

In phrases

titley and binder (n.)

a glass of beer and a piece of bread and cheese.

[UK]cited in Partridge DSUE (1984).