The issue is Netflix and an error on their end as they have incorrectly black listed the temporary IP address given to you by BT as a VPN. Even though you can get a new IP by rebooting the router, it probably won't work as Netflix would blacklist a subset, meaning a whole bunch, being the ones in your area.
Had the same issue, did everything in their help page, called Netflix and all they could do was tell me to call BT and do what the troubleshooting page said again. Tried to explain to the useless robot operators at Netflix support that networking protocols are my job, and them trying to fob me off with excuses was like them telling a brain surgeon how to do brain surgery. I tried to explain to them what the issue was (they have an incorrect blacklist and giving my expert services for free), but they just passed me round from operator to operator and eventually hung up on me (very rude of them).
Netflix support is useless, they don't even give you a way to email them, so if they don't resolve it, or take too long, dispute the credit card transaction for failure of service and get a refund. If it doesn't work the following month, you will just have to cancel your subscription to Netflix as it is likely a long term/perminent fault.
