I entered my number in the username box, along with my password, and here I am, using the internet with no problems.
Well, I am a BT customer but I don't know my log in details. Both my Mac and iPhone connect by typing in my mobile number on their respective browsers. I understand that if I want to use BT Openzone on my iPhone it asks for the mobile number and network, and then it's meant to take me to an O2 log in screen. It doesn't do this.
It turns out that the password I enter on the BTOpenzone screen can be anything I want it to do be - it's got nothing to do with my O2 password. Also, just to see if it did work, I tried logging in on my MacBook with my girlfriend's phone number (who is on Orange and has no BT account) and that worked too.
The other possibility is that you are being phished. Anyone can set up a network named BT OpenZone, which puts up a splash page similar to the BTOpenzone one and asks for details - they could then (for example) intercept all info that you send and receive on that connection. Are you sure you are definitely connecting to an official BT Openzone hotspot? Perhaps try another hotspot to check if that works.
The MAC address of the iphone will be registered on openzone and you can't register the laptop on it with the same details as it has a different MAC address.
If you have WIndows OS on the MAC and Connection manager 2, you can connect to the Openzone hotspot using a PAYG or Contract USB modem from O2