Check the online newspaper sites. He often gets a mention as a general nuisance and petty criminal who likes a drink or several.
19 November 1870, Cambridge Independent Press
"Dry Drayton.—William Badcock was charged with allowing a mare to stand on the highway without anyone to attend to it. Fined 2s. 6d. and expenses."
29 June 1878, Cambridge Independent Press
"DRUNKENNESS. William Badcock, of Dry Drayton, was charged by E.S. Wilderspin with being drunk and disorderly at Longstanton, on the 10th inst. P.s. Wilderspin said: On the day in question, at about ten o’clock in the evening, I heard a noise...."
13 July 1888, Cambridge Independent Press
"THREATENED A TRAVELLER. William Badcock, described as a traveller, belonging to Dry Drayton, was charged remand from the Occasional Court House on the 3rd lust., with threatening Emma ..."
Available from any of the sites that provide newspapers, e.g. FindMyPast, GenesR, or the Newspaper Archives site themselves.
There are quite a few. It'd take a while to check/double check each offender is the same fella and not his father/son/brother (on the basis he's likely to be named after his father/uncle and to name his own kids the same).
ALSO:
Looks like somebody else has plotted him, from birth to death, including a hospital visit and his two marriages, here - about half way down this PDF.
http://www.etma.org.uk/musicianpdf/1831-1840.pdf