Eoin,
That's definitely not something we've seen before and I'm not sure of the exact cause. First off, the following page is returning a 403 error. That needs to be fixed and *could* be the cause of the problem:
uglyfashionmedia.com/components/com_jfbc...sets/jfbcchannel.php
Beyond that, can you check that you have re-run Autotune since you added the SSL certificate and make sure that your domain, Web URL, and all other settings match the recommendations? Also, is it possible to disable SSL temporarily and try on the non-SSL site to see if that works? That will help narrow things down.
When the page loads, we insert some Javascript on the page for the variable "jfbc.base". That is getting set correctly. We use that value in our jfbconnect.js file to set the redirection to the loginFacebookUser page that you're seeing. Somewhere in there, the value is either getting removed, corrupted, or somehow changed. Again, I've never seen that before, so if the above doesn't work or narrow things down, we'll have to investigate more.
Let us know what you find!
Thanks,
Alex