It's tough to limit access to a website by browser because there is no 100% foolproof way to do it.
Your first problem is user-agent spoofing. Browsers can identify themselves with any user-agent they want to. Browsers with extensions all seem to have one that makes doing this trivial. If someone with IE6 or IE7 changed their user-agent to be that of IE8 or Firefox they'll get into a website.