Piers, I think you may be right about Susan going along with a partially staged episode on BGT. And I don't fault them, or her, for that.

Susan's looks are what they are, but normally one would expect that a woman "auditioning" in a world that values youth, beauty, and glamor would have her hair and makeup done professionally and wear the most flattering outfit she could muster for that audition. The fact that Susan came out on the BGT stage in a kind of frumpy-looking dress that looked washed-out on TV, with an almost nonexistent "style" to her hair, and looking like she hadn't paid any attention to makeup - that says to me one of two things: Either she and the show producers agreed that she should capitalize on the ugly-duckling-into-swan thing or she simply wanted to defiantly declare to the entertainment-seeking public, "This is who I am, warts and all.   Take it or leave it."   I suspect it was a little more of the former than the latter.

I don't know that much about how BGT (or America's Got Talent) works, but on the "Idol" shows that Cowell also does, all the contestants who get TV time at all have been seen and heard by the judges.   And in both shows (Got Talent and Idol), some contestants are put in front of the viewing public for comic relief (e.g., the "bad singers" portion of the aired Idol competition), and occasionally a contestant is put through to the semifinals (where the public gets to vote) despite "not looking like a pop star," because the show's producers think the contrast between image and voice makes for good entertainment.
(In American Idol's second season, the competition was basically between 6'1"/145 lb "geeky" Clay Aiken and 6'3" 350 lb "teddy bear" Ruben Studdard: both guys had big, gorgeous voices, but neither "looked like a pop star," and the show capitalized on the contrasts.)   
I get the feeling, from watching America's Got Talent, that the judges on that show have NOT actually heard and seen the contestants before they perform for the TV audience. But rest assured that there are plenty of people involved in producing the show who HAVE auditioned and chosen these people.   Someone who looked like Susan Boyle would never have made it onto the televised portion of the show unless she was either so BAD that her spot on the show would have been comic relief or so GOOD that people would be astonished that "THAT voice is coming from THAT body and face!"    The BGT judges naturally knew that Susan was going to be one or the other.   (No one with Susan's visual image and a so-so voice would have been selected to appear on the show.)   
Piers and the woman judge may have been expecting Susan to be yet another comic-relief act and were pleasantly surprised when she turned out to be the other option. I think Simon Cowell, with all his years dealing with Pop Idol and American Idol, probably really did "know" the minute she walked out on stage that he was about to hear something extraordinary.    Not because that was "staged," but because he knows how the TV show works.

Genie

PS,
Leo, you're so right. Susan Boyle isn't anywhere near the grotesque that some reviews are making her out to be. She's a rather average-looking 40-something woman in an entertainment world that more and more seems to expect, even demand, that women be a size 4 (with a DD bra size) 20-something with "chicklet teeth."    Walter Mathau can be paired with Sophia Loren as a romantic couple, for instance, but not Bea Arthur with Paul Newman.