Green’s Dictionary of Slang

threepenny bits n.

1. diarrhoea [shits, the n. (1)].

1972		Dodson & Saczek Dict. of Cockney Rhy. Sl.
1985		B. Humphries Traveller’s Tool 80: That way you’ll be pretty sure a meal there won’t give you a dose of the threepenny bits.

2. a woman’s breasts [tit n.² (1)].

1963		K. Waterhouse Jubb (1966) 25: It’s full of ’em. Birds! [...] Shoulda seen this one with the big threepennies.
1972		Dodson & Saczek Dict. of Cockney Rhy. Sl.
1978		Maledicta II:1+2 (Summer/Winter) 118: He [...] also lists: [...] Threepenny Bits Tits.
1980		Barltrop & Wolveridge Muvver Tongue 11: One or two rhyming expressions existed – ‘threepennies’, for ‘threepenny bits’, and ‘Manchesters’ – but were never much used.
1999		Guardian Weekend 25 Sept. 24: Tailored to flatter our thr’penny bits, which were big.
2002		D. Shaw ‘Dead Beard’ at www.asstr.org 🌐 To tell the truth I couldn’t care less about Dionne and Lingers, they’re both bad news but something about Dionne has got on Monica’s threepenny bits.
2013		K. Sampson Killing Pool 259: Does he [...] tell them they’ve got ‘ten out of ten threepennies’?

In phrases

give someone the threepennies (v.) [fig. use of sense 1]

to annoy, to irritate someone.

1963–74

B. Humphries Barry McKenzie [comic strip] in Complete Barry McKenzie (1988) 78: I can’t stand toilet talk from sheilahs — it gives me the threepennies.