I've had our web guy have a look at the site and he's found a neat workarout I thought you may find useful for future occurences of the same issue. Here's what he had to say:
As a complete "dodgy-brothers" bandaid while I sort this out, I have duplicated the wp-login.php file and called it login.php and changed all references within login.php to point to itself, so if you go to:
You should be able to login via this end point and get some work done while I sort this out - I tested it out and seems I can login and logout. Funny thing is, the "logout" calls the original wp-login.php file and it is fine!