I don't know what a "log book" is and what is precluding you from adding it to your app (we bought a used Y and I found the process to add it to our app was very simple -- I think we just needed a bill of sale or something similar, and it was added instantaneously). Maybe this is a UK requirement.
Anyway, if there really is some kind of impediment you can't get around, your best bet is going to find third-party charging stations to charge your vehicle. I believe the Tesla connector in Europe is compatible with third party charging networks. If you were in the US, this would be more problematic (for now).