Replacing the brake light switch seems to be a popular cure for cars flipping into Engine Failsafe Mode.

Quite a few years of XK8's use P/N LJB6420BB

I searched today and found a typical price to be in the $85-$95 price range.

I've had very good luck with these guys:

http://www.jaguarparts.com/partscat.html 800-783-5247

Their parts counter price was $95 but their internet price was $59.50!

I've bought several parts from them (unfortunately!) and have been very happy with the service.