Solved by uninstalling .NET Framework 4 Client Profile. Updates then work.
Tried to repair the above first, but only uninstalling works.
It gets re-installed by updates (seeming after the Malicious Software Removal Tool has run!?) and Updates stops working again.
Not sure what's going on but at least I can get the latest updates. It's just crazy that I have to keep uninstalling the .NET Framework each time to update.