Safari doesn't log into Orange Site.

I have Safari 6.0.5 running on Mountain Lion 10.8.4, and I try to login to Orange site to check my mobile phone bill. Unfortunately I press the 'login' button and it just refreshes the actual login page.. It works fine on every other web browser, But I actually prefer Safari's interface and design.. I am thinking of waiting for the release of OSX Mavericks this fall/autumn. But that seems kinda far to wait. I tried downloading Safari on my Windows computer but it works fine! :/

Any help would be appreciated, Thanks in advance.

-Shock