I had the same issue and managed to resolve, so posting here in case useful to others.
Netflix account hacked and login email address changed. Netflix try to talk you through verifying through the Netflix app on another device. Whoever had taken control of the account had "signed out all devices", so I could not get into the app.
They will then verify via payment details, but if you are billed through a third party (EE) they cannot and will ask for a six digit service code. They have screen prompts to try and talk you through logging into EE to find this in the manage products section. These bear no resemblance to what is on the site and the code cannot be found. They then tell you to call EE.
EE did not know how to get the code and proposed deactivating and reactivating the Netflix extra. This would allow you to go in and enter your email afresh to get access. I DID NOT DO THIS. My suspicion is that this would result in Netflix saying there is no account with that email and setting up a new one. While you would stop paying for the old account, I suspect it would leave your old profile and viewing history on the old account under the control of the hackers.
SOLUTION: I eventually discovered that an EE TV Box (But not an EE Apple TV Box) that has been linked to a Netflix account cannot be signed out/deactivated. I had an EE TV Box Mini that was supplied originally that I do not use in favour of the EE Apple TV Box. I plugged this in and it did indeed access the Netflix app. In the app I was able to find the service code (it also showed me the email address that had taken control of the account (which Netflix refused to disclose to me). When provided with the code, Netflix changed the email back and sent a password reset.
