Green’s Dictionary of Slang

Burton-on-Trent n.

the rent.

1910		Eve. Teleg. (Dundee) 3 Aug. 4/1: 'What's the Burton?' [...] 'Burton-on-Trent' means rent.
1932		‘P.P.’ Rhy. Sl. 13: Goin’ to take a ‘ball of chalk’ up the ‘frog’ to pay the ‘Burton’ or there’ll be a ‘bull and cow’.
1960		J. Franklyn Dict. of Rhy. Sl.
1979		R. Barker Fletcher’s Book of Rhy. Sl. 25: Being very short of bees and honey, and unable to pay the Burton-on-Trent.
2002		B. Kirkpatrick Wicked Cockney Rhy. Sl.