Okay, a solution for Windows 7 X64 which has worked for two machines:
Listed with direct links under "Alternative Fix (June 2016)"
at this superuser post (via superuser link above):
my problem was not only very high CPU usage [windows update check/svchost], but also inability to find *any* updates
I can report this working on another Windows 7 machine (not mine) with similar problems.
(Was my sister in Canada: she got an IT guy to look at it, they had no solution; so I enjoyed being able to say I probably know how to fix that...