The expression Butler English is confined to Indian English. I searched through many of the corpora at english-corpora.org including COCA, BNC, NOW, and GloWbE. The American English (COCA) and British English (BNC) corpora returned no results. Among the other corpora, I only found about 10 results, all of which were from India, such as this news article from New Indian Express:
Rao even heckled Naidu, saying that with his ‘butler English’ and little knowledge of Hindi, he couldn’t do anything in national politics.
The book Far East from 1943 gives a very striking impression of the environment in which the expression originated:
[D]ue to the caste-system, different communities are allotted various categories of work, and that it is impossible and irregular for a man to substitute for another; thus six servants are needed to do the work undertaken in England to-day by one heroic aged peeress. Any Englishman, living however quietly and simply in India, will have at least six servants: a cook, a butler, a laundryman, a sweeper, a groom, a gardener and perhaps one other.
This means that in India (at least at the time) a native (British) English speaker would likely have employed an Indian butler (who would not have been a native English speaker). Contrast this with English-majority countries: the average native English speaker there would not have been able to afford a butler and those who could afford it could easily find a native speaker to employ. In fact, 1943 also brought us Batman's Alfred, who is a pretty good example of a butler stereotype found in American (and perhaps also British) culture: British, intelligent, and "refined and well-spoken".
Due to this stereotype, you are very unlikely to be understood if you use the expression Butler English in American or British English. The most common way to refer to bad English would just be broken English.