Green’s Dictionary of Slang

muffin baker n.

[rhy. sl. = quaker n.; orig. misunderstood by Hotten and entered in early edn as a ‘Quaker’ in religious meaning]

excrement when hard and retained.

[UK]Hotten Dict. of Modern Sl. etc.
[UK]Hotten Sl. Dict.
[UK]Sl. Dict. 367: Muffin baker, a Quaker (slang term for excrement).
[UK]J. Franklyn Dict. of Rhy. Sl. 97/2: muffin baker A quaker [...] applied to excrement.
[UK]Partridge DSUE (8th edn) 764: A ‘quaker’ in the Cockney low s. sense, for excrement long retained.