BT Wi-fi is a service which gives access to wifi hotspots provided by participating broadband customers and commercial establishments (sometimes identified with an obsolete BT Openzone SSID). Fon is a separate organisation which provides wifi access between members. They quite separate and entitlement to one does not provide access to the other.
On the other hand, BT Broadband customers who are opted in to BT Wi-fi are afforded access both services. In return, their home hubs broadcast a separate SSID for each service, but independent users can only connect to the one appropriate to their entitlement. So the simple answer to your question is "Yes", although BT Fon is not an entity.
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