Our Solution - Bottom Element Replacement - now works perfectly
Had a very similar issue and solving it was fairly simple once I had summoned up the courage. 
Switch off all electrical supply to the oven including at fusebox. 
You need to take off the back cover to the oven.
Using a voltmeter check for resistance in all the elements - a failed element will give you an 1 reading a working element will be very close to zero. 
In our case the bottom element had failed. 
Unscrew the 2 retaining screws for the element and work out how to gain access to it - this may differ from oven to oven - on ours you had to undo a panel in the storage section below the oven - a bit fiddly but not impossible. 
Repolace the element - got ours from 
http://www.partmaster.co.uk/cgi-bin/product.pl?PID=955111&query=Kenwood%20CK780%20Element&model=CK780&path=78825,261565:261646
Put it all back together. 
It now heasts to 250C again in about 20 mins. 
Hope that's helpful
                
 Pete
                
 October 2008