First use of "judge, jury, and executioner"

Solution 1:

The earliest I can find is Daniel Defoe, "Memoirs of the Church of Scotland" (1717)...

...make every private Sentinel, every Musquetier, both Judge, Jury, and Executioner.

For future reference, OP might like to hang on to this Google Books link. Enter the target phrase "in quotes", then use Search Tools to keep whittling down the date range until you've got the earliest one. Re-search without quotes, to find any earlier instances phrased slightly differently.

Solution 2:

Slightly earlier than the Defoe reference, we have William Congreve's play, The Double-dealer, published in 1706 but first produced in 1693. It contains the lines:

But in this Court, what Diff'rence does appear!
For every one's both Judge and Jury here;
Nay, and what's worse, an Executioner.

Solution 3:

Contemporary with the quote from Defoe is this from a political monthly:

"...the King issued out a printed Order, for all Whigs to shoot or destroy, by the Way they would, any that should be charged with Concern in any Riot in Time to come; which constituted any malicious Man, the Accuser, Judge, Jury and Executioner of his Neighbour;." - The Political State of Great Britain, for October 1717 (Vol.XIV:398)

Solution 4:

Published a year before Congreve's The Double-dealer, but evidently written 12 years after Congreve's play was first produced is William Grimston's play, The Lawyer's Fortune: or, Love in a Hollow Tree (1705), which includes these lines:

Florida. Oh! Thou wild Monster of Mankind, whose Venom Breaths it self thus to the Destruction of they Betters!

Friendlove. Peace, Madam, If I had Kill'd him it had been but Justice.

Florida. And must you make your self Judge, Jury, and Hangman? tho' the last might be a proper Office for you, yet I am sure you have no Right to the former; Oh, thou Villain!

This formulation—with a hangman in place of an executioner—thus appears to have reached print first, but not to have been presented to audiences first. A note in the Dictionary of National Biography (1903) observes that Grimson's play was "ridiculed by Swift and Pope," suggesting that it may have provided "judge, jury, and hangman" less of a boost into popular usage than Congreve's play may have done for "judge, jury, and executioner."