Green’s Dictionary of Slang

mean-faced, pinched features.

1888		J. Runciman Chequers 80: Garn, you farthin’ face! Shet your neck.
1995		P. O’Keeffe Down Cobbled Streets, A Liberties Childhood 127: ‘You’ve a little farthin’ face,’ she would declare as she wound the rags around my stubborn hair.
1999		G. O’Neill My East End (2000) 79: My father’s generation of East Enders – he was born in 1919 – do not speak the dull, uniform, flat-vowelled Estuary English [...] He will still use what is essentially Victorian idiom – phrases such as ‘daddler mooey’ and ‘fard’n face’.

the smallest available portion of ice-cream as sold by street vendors.

1898		Sunderland Dly Echo 4 July 2/8: The ‘hokey-pokey,’ ‘farthing taster,’ and so forth [...] sold by ice-cream vendors [...] are pepared in filthy hovels.
1909		(ref. to 1870) in J. Ware Passing Eng. of the Victorian Era.