Virtually all log-in problems are to do with privacy settings when using Internet Explorer as your browser (as most people do). There's a paragraph on the front page of the site headlined "Can't log on? Here's probably why" which gives a potted version of what follows below.
If you're using Internet Explorer, go to Tools and then Internet Options and click on Privacy - put the slider to one notch above the bottom (as illustrated in the screenshot below) and all should be well. Changing this setting won't affect the security on your computer. (If the slider's already on Low or lower, it may be some other aspect of security or privacy that needs fixing to get you into the site.)
If re-setting the privacy slider doesn't solve the problem, remember that usernames and passwords are case-sensitive so make sure they're entered as you submitted them. It won't matter whether you're using a school or home system - the e-mail address submitted when registering was just for verification.
The setting needs to be lowered so that passwords can be recognised. Passwords are necessary on this site to allow you to use the resources with your students when you think it's best (rather than when they do).
If you can't change settings because you're on a school or college computer, other suggestions have included using Firefox or Google Chrome as a browser for this site - they don't have the privacy setting issues and the software for the former can be quickly downloaded from http://www.mozilla-europe.org/en/firefox/.
If you have technical folk at school to help, I am told that one school managed to get the website to work in school without lowering any of the privacy settings. The network manager added http://s277881626.websitehome.co.uk/emporium as an exception in their internet filtering software (adding www.edexcelmaths.com doesn't have any effect because the website actually loads an iframe pointing to http://s277881626.websitehome.co.uk/emporium).
The above is the limit of my IT expertise at present, I'm afraid - but changing the settings has worked for many others who have had difficulties. You may, of course, need to involve your school or college IT people or accept that you can only access this site at home.
Let me know if any of this works - if not, I'll see if there's anything else that can be done. If you need to contact me, please remind me of your username if you haven't already done so.