Weird intermittent /wp-admin/index.php was not found error

Hi

Since upgrading to 4.6 I’m getting an intermittent “The requested URL /wp-admin/index.php was not found on this server.” 404 error when doing stuff in admin. If I refresh, the correct page will load, so it’s not any of the problems to do with URL or site location on server (as far as I can see).

I think users are getting 404 errors, too – but it’s hard to be sure. The logs do not show anything conclusive – and it’s hard to reproduce (typical intermittent error).

I’ve removed all plugins – still get the problem. Reinstalled WP, still get the problem.

Site is https://www.gln-scouts.org.uk

Anyone seen anything like this?