Green’s Dictionary of Slang

stick up v.3

to hold one’s ground in an argument.

[UK]Farmer & Henley Sl. and Its Analogues.

In phrases

stick up to (v.)

to challenge, to oppose, esp. when one is ostensibly at a disadvantage.

[UK]Hotten Sl. Dict.
[UK]H. Baumann Londinismen (2nd edn).
[UK]Partridge DSUE (1984) 1153: [...] coll.: from ca. 1840: dial. till ca. 1860, then coll.