If I rock my bike back and forth with the front brake applied, there is noticeable play on the 1" steerer tube on top of the head tube. The stem actually slides back and forth on the cap sitting on top of the bearings. I'm pe-loading the bearings OK. Does the top bearing cap need to have a hole in which the steerer tube fits very neatly? The cap I'm using has a hole a bit larger than the diameter of the head tube. Maybe this is where the problem lies? Any suggestions welcome?
Something is wrong. Either the headset is the incorrect one or there is a part missing. Often there is a tapered ring that wedges the steerer into the headset.
Take to your LBS for checking
Sorry for posting the obvious but have you got the right number of spacers on the steerer? The stem needs to be a few mm higher than the steerer tube for you to preload properly