So if you try to log into the site from the .co.uk domain, the cookie still gets set for the .com domain and therefore because you are actually accessing it via the .co.uk domain the two don't match and the site still thinks you are logged out.
I hope that made sense.
A possible way around this is actually to disable cookies in your browser. The site will then be forced to use it's other method of login, which uses a serverside session and if this is active you will see an ID number in the site URLs. Using a serverside session, it shouldn't matter which domain you access the site from.
I will look into a proper solution to the problem though.