Sarah McLachlan released a cover of this song on her Rarities, B-sides and Other Stuff album.
Normally, for a cover to be worthwhile, the artist needs to take the song and add their own personal style to it. Otherwise, what's the point? After all, you could just go out and purchase the original. The Bangles' cover of Hazy Shade of Winter an example of a worthwhile cover. Also, Weird Al's polka medleys of popular songs work because the style is so completely different.
McLachlan didn't change the style of this song very much at all, but in this case, it worked extremely well. It starts sparse, quiet, thoughtful, almost pleading tone, but then her anger builds slowly, until it eventually climaxes with a "heretic-screaming-from-the-stake" ferocity. McLachlan manages the emotional range far better than Andy Partridge, and while XTC's original is great, McLachlan's is even better.
Of course no American radio station will ever play it.