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After a factory reset, the wireless password would default to the one written on the home hub, so if you have changed it, you would not be able to connect via wireless until you enter the original password as shown on the home hub.
So, asking for a friend here, I would be able to access the router settings and change them (let's say to configure the router for Plusnet BB).. all remotely without needing to connect to a computer via Ethernet?
BT Home hubs are locked to BT Broadband, so cannot be used on Plusnet.