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If you go to Settings --> Wireless & Networks --> WiFi, you will see a list of all networks in range of your device.
The BT Openzone SSID is either BTWiFi or BTWiFi-with-FON, and your device is connecting to one of these.
You will also see at least one other SSID which you should recognise as your private network, if you long press that SSID you will get the option to connect, tap it and your device will switch to your network.
If you then tap on each of the other SSIDs that you don't want to connect to, you will get an option to 'Forget Network'. Your device should then only connect to your private network.
As a matter of interest, if you are a BT Broadband customer you may have unlimited access to BT Openzone/BTWiFi. I use it at home to avoid exceeding my 10Gb usage, and from BTWiFi hotspots when out and about.
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Hope this helps.
