I\'m making a members area for my site and I have it already running. I authenticate members using mysql and php and this works really well.
But now problems occurs,
Check out Using PHP/Apache to restrict access to static files (html, css, img, etc). I think the approach taken there is pretty similar to your problem.
It seems like you are confusing authentication (where you provide some way to login) with HTTP authentication (where you specifically use the HTTP protocol to authenticate, and the browser shows a popup to the user).
You probably want the former so you can style the login page. In that case you'll have to use PHP or some scripting langauge to check that the user is logged in. fpassthru or readfile can be good solutions for some web sites; they're fast and optimised for this type of work.
If you really want to do the file handling work in the web browser and not in PHP, one solution can be to create unique, short-lived filenames. You can for example create hard links to the file in PHP using link and then redirect the user to the temporary filename. Store the hard links in a database and remove them after a short while.