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Normally, if you are opted in to BT WiFi, then you cannot turn the wireless off on your Home Hub. If you can turn it off, then this suggests that you are opted out of the BT WiFi service.
This page https://www.bt.com/wifi/secure/status.do?s_cid=con_FURL_btfon/status can be used to check your status.
It's nothing to do with turning off your router. See if the BT WiFi helpdesk 0800 022 33 22 can help but please report back here if that doesn't get it sorted.
EDIT: In view of ectophile's comments I should explain that I took it that the hub was being switched off.