Extensive searches of Burke's published works and correspondence, summarized by quotation researchers and noted in reference works such as the Yale Book of Quotations, find no instance of the line. A related sentiment appears in John Stuart Mill's 1867 inaugural address at St. Andrews: bad men need nothing more to compass their ends than that good men should look on and do nothing. The exact wording appears only in twentieth-century attributions.
The line circulated anonymously in early twentieth-century speeches and print, acquired Burke's name by mid-century, and was cemented when public figures repeated it. Once a statesman-shaped author attached, the quote became unfalsifiable in casual use.
The attribution is not random: Burke did write that when bad men combine, the good must associate, in Thoughts on the Cause of the Present Discontents (1770). Culture filed the punchier fake under the man who wrote the clunkier real one.
If a democracy's most quoted warning about apathy was ghost-written by repetition, who is minding the quotation shelf?