What can help, is to go into your phone`s wifi settings, and delete any saved wireless networks that have BT Wif/FON showing against them. Once you have removed them all, try reconnecting to BT Wifi again.
What tends to happen, is that a number of duplicate connections are stored on the phone, with the same SSID, and when it tries to connect, it selects the wrong one, and there is no connection.
This can happen if you come into range of other BT Wifi hotspots, and because they are open networks, the phone connect to them, and they get stored. This confuses the phone when you then try and connect to a nearby one.