All sorted by my LBS ( in an unprecedented 15minutes of competence).
I thought it was going to be an expensive/tedious thing to fix:
BTW some of these parts have flat bottoms but most have various small steps on them. Obviously if you get a new one it needs to be the same shape underneath, else there will be trouble.
Yes, I was afraid of that. Tried to get a proper Cane Creek, but they don't seem to do them anymore (phoned distributor, etc ...).
It looked the only option was to buy a complete unit with a lower stack height - min cost £23 even on the bay. Plus fitting time.
So I was v happy when the LBS found an unbranded-but-comaptible part in their bits box and fitted it FOC!
They also pointed out that the actual
bearings on this bike are a Specialized-specific component. Bloody typical. Worth knowing for the future. I shall not be seeking out bikes with integrated headsets as my next purchase ...