Spirit of sharing
In SITE ADMINISTRATION >USERS> PERMISSIONS >DEFINE ROLES (choose Student)
I unticked: View user profiles :: moodle/user:viewdetails
This has now disabled the viewing of profiles for students other than themselves.
I'm not sure whether 'disabled' was the default for Moodle all along, and someone changed it - or if I've changed a default setting. However it seems to have worked ie. disabled students from viewing profiles and thus emails of other students.