Canon support suggest uninstalling, disabling Windows Firewall, and any other anti-virus software and reinstalling. This DOES NOT WORK, however often you try it.
The actual solution is to right-click on the exe file for EOS Utility, and choose compatability mode. It switches to Windows 8 Compatability, and when tested opens, as it should, as opposed to doing nothing when previously you clicked on it, following the Windows 10 update.
I hope people with this problem find this solution before they go wasting too much time faffing around with the insoluble offering by Canon Support.