Green’s Dictionary of Slang

blind cobbler’s thumb n.

In phrases

face like a blind cobbler’s thumb (n.) [? covered in pockmarks, resembling needle-pricks]

a derog. description of the face of an unattractive person, usu. a woman.

[UK]T. Pratchett Feet of Clay (1997) 230: That’s Nobby [...] Face like a blind carpenter’s thumb.
‘S’ ‘Hungover Gloss.’ at HairyTongue.com 🌐 Face like a blind cobbler’s thumb [phrase] Used to describe the unfortunate looking young lady that takes your fancy after 8 pints of Stella: ‘She’s got a face like a blind cobbler’s thumb, mate!’.
G. Joyce 14 Jun. on GrahamJoyce.net [blog] Naturally I protested in Ye Olde Englishe style, only to be persuaded onto the street by a bouncer with a face like a blind cobbler’s thumb.