The result was that Task Scheduler and Windows Update both stop working (the nice dialogue box comes up to inform me of this fact) and the associated error code is not one that exists in any Microsoft site.
The get online help only returns advice for general errors in Windows Update (not surprising as the error code has no documentation associated on the Microsoft Site so I can't expect the online help tool to find anything for me).
I installed all the hotfixes that cured performance issues BEFORE I installed sp1 - so I suppose it may be that all I gained from sp1 was security and bug fixes.
I have since added other updates successfully (I guess sp1 is not yet on Windows Update) but I think I will wait a few months before trying again, perhaps then if I get the same issues afterwards there will be some advice out there to help me.
Some of the "similar" problems reported state that Background Intelligent Transfer Service (BITS) is the root cause, and that deleting (after boot into safe mode) some temporary files used by this process will cure the problem, but this did not appear to help me.
Normally I am quite anal about applying updates but in this case I will keep applying all the minor fixes offered by Windows Update and hang back on sp1 for a while until is becomes essential as a prerequisite for other patches.