HTTP authentication only offers a method of password protecting HTTP access to your sensitive data.
This is fine for most purposes but it will not protect your data from being accessed by anyone who has access to the server via other means (someone with physical access, root access or someone who manages to exploit a security hole in any of the server's running processes for example).
You may consider this overly paranoid, but 'how secure' it needs to be depends on how sensitive the data is. How disastrous would it be if someone was to get hold of your client's passwords? What damage could be done with them passwords, etc?
Personally if I was doing this, I would additionally encrypt the data stored on the server, so even if someone gets hold of it, it would be next to useless to them to get anything out of it, or at least make it very troublesome for them. Your PHP can do the decryption when you supply it with a decent passphrase only you will know. Also make sure you use SSL when accessing your PHP page so that nothing is passed over the net in plaintext.
As kakki says though, there is no "absolutely foolproof" method... you can only make sure you get as close to foolproof as needed for the data your storing.