Green’s Dictionary of Slang

penny bun n.

[rhy. sl.]

1. one; one penny.

[UK]Partridge DSUE (8th edn) 234: cockle to a penny [...] penny = penny bun.

2. the sun.

[UK]J. Franklyn Dict. of Rhy. Sl.
[UK]Dodson & Saczek Dict. of Cockney Rhy. Sl.
[UK]R. Walton ‘Cockney Jack and the Beanstalk’ 🌐 The next front and rear, when Jack’s grounding was up, he stepped outside for his first breath of penny bunshine in a long, long nickle and dime.

3. a son.

[UK]J. Franklyn Dict. of Rhy. Sl.
[UK]S.T. Kendall Up the Frog.
[UK]Dodson & Saczek Dict. of Cockney Rhy. Sl.