As a fair guess, I'd say that as you have to present the ID you provided when booking at check-in, then if the booking details on file don't match the ID handed over, you don't fly.
The only caveat that I can think of is that it's a case that you booked some time in advance & your passport, for example has had to be renewed in between.
However, I do know that in the US when you use a credit card as ID (even a UK card) at self check-in, if it is renewed between booking and travel, then that is not a problem, as I've done that, but I was quite surprised that it did, especially as I was checking in for a return trip back home.