Several (*cough*) people have asked this:

http://www.flyertalk.com/forum/showthread.php?t=593888

The answer appears to be: "45cm x 35cm x 16cm, the size of a small laptop bag, inclusive of wheels and handles". Class of service makes no difference. It's not the airlines forcing these ridiculous rules on people in the first place, and it's being policed by BAA at the security checkpoints. They are being strict.