E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
Hanged, drawn, and quartered, or Drawn, hanged, and quartered. The question turns on the meaning of drawn. The evidence seems to be that traitors were drawn to the place of execution, then hanged, then drawn or disembowelled, and then quartered. Thus the sentence on Sir William Wallace was that he should be drawn (detrahatur) from the Palace of Westminster to the Tower, etc., then hanged (suspendatur), then disembowelled or drawn (devaletur), then beheaded and quartered (decolletur et decapitetur). (See Notes and Queries, August 15th, 1891.)
If by drawn is meant conveyed to the place of execution, the phrase should be Drawn, hanged, and quartered; but if the word is used as a synonym of disembowelled, the phrase should be Hanged, drawn, and quartered.
Lord Ellenborough used to say to those condemned. You are drawn on hurdles to the place of execution, where you are to be hanged, but not till you are dead; for, while still living, your body is to be taken down, your bowels torn out and burnt before your face; your head is then cut off, and your body divided into four quarters.Gentlemans Magazine, 1803, part i. pp. 177, 275.