The dictionaries and glossaries I've look at differ considerably in what they say about English appearing with a lower-case e when using the word for spin or side.
No Mention: (Assumed upper-case only)
Print OED: no mention
Print The New Oxford American: no mention
Online M-W: no mention
Online Lexico: no mention
Online Oxford/Google (FreeDictionary): no mention
Qualified upper- or lower-case:
Print Webster's New World: [sometimes e-]
Print Collins: often not cap.
English: alternative form of “english.”
english: term usually used
to refer to sidespin applied to the CB, but can also be used to refer
to any type of spin applied to the CB (e.g., with draw and follow
shots).
...
english-induced throw: same as “spin-induced throw.”
english transfer: same as “spin transfer.” Billiards Terminology Glossary
Lower-case only:
Wiktionary: entry is in lower case on a page of Glossary of cue sports terms
Looking at a few pages of hits for "put/putting english on the ball" in Google Books, the lower-case e is less common, but present.
You and your opponent each have a control unit. Each unit not only
moves a square, but can put english on the ball when it hits it. Popular Science (1972)
Marie stood rigidly at a machine next to me, moving only her fingers
on the flippers as if entranced, hypnotized by the lights and the
computer gibberish, while I leaned into my machine or jolted it with
stiff arms sometimes violently trying to put english on the ball or
achieve a greater bounce off the bumpers. Blood Confessions (1992)
Studs, unconscious of everything, put the balls before him, ran the
table, feeling a sense of skill and power as he made ball after ball,
planning shots ahead, putting english on the ball to get position,
feeling a complete mastery. Studs Logan (2001)