My problem has gone away. I think that BT's (or their partners') security algorithms look at the geographical origin of a connection and may prevent access based on that (e.g my vpn may route through Iceland). If I do have the problem I disconnect my vpn and the reconnect once I am in to email.
I am not a BT Sport customer so don't know if that will work the same way.
Also, before you rush to another supplier you might want to check if they have the same policies 🙂
Bt Sport won't work regardless of location. I'm not bothered about the services anymore as long as my broadband works. Fed up with BT below par customer support so leaving for that reason. I have other means of streaming content now 😉
I regularly change the route my VPN uses ... and most ISPs have been used to send spam so this "solution" does note work.
Routing through Iceland or Sweden doesn't seem to make a difference