Green’s Dictionary of Slang

a basin, a basinful.

1960		J. Franklyn Dict. of Rhy. Sl. 49/1: Charlie Mason Basin Early 20C [...] It no longers refers to an article of kitchen ware, but ‘I’ll have a Charlie Mason’ means ‘I’ll have a basin full’; that is, a try, or a share, or a ticket in a sweepstake.
1969		S.T. Kendall Up the Frog.
1972		Dodson & Saczek Dict. of Cockney Rhy. Sl.
1992		R. Puxley Cockney Rabbit.
2002		B. Kirkpatrick Wicked Cockney Rhy. Sl.