Since updating to 2.9.62 right clicking on a link does not bring up the JCE context menu, but instead the Windows context menu (which is of no use). To edit a link I have to use the icon in the toolbar.

This is using Firefox - haven't tried other browsers. Perhaps linked to the change you made for mobile browsers mentioned in the changelog?

Please see if this is helpful:
https://www.joomlacontenteditor.net/support/forum/104674#p104680

Thanks Ryan, but none of those things in your list is the case and the problem only cropped up when I installed 2.9.62. I have 2.9.61 on another website and the issue doesn't occur there.

Using Edge the problem doesn't occur with 2.9.62 either, but I prefer to use Firefox.

I've now installed 2.9.63beta1 on a test website but no improvement.

Ah, looks like the problem was caused by a Firefox plugin for simulating using a mobile device. This was set to Default, but selecting a specific Windows/Firefox setting fixed the problem. So panic over! Sorry to bother you.