My experience has been I can access the hub just fine without an internet connection, but I have not had that happen at the same time as a power failure. It seems like if you could address this issue HE would have worked as expected, though you probably would have had to manually reset the time via the UI. I'm guessing (but don't know for sure) the issue there is HE uses a software clock rather than a hardware clock and relies upon a periodic time sync to adjust for drift. I've read in other threads (see below) that if the hub loses power when it comes back online and can't do a time sync from an NTP server it just resumes where it left off, which would make sense with my software clock theory. Sounds like what happened in your case.
Not familiar with the BT (British Telecom??) router but the fact that it stopped working entirely without an internet connection seems less than optimal. A UPS on your HE would probably help quite a bit. It might not keep the whole thing running for 6 hours but it might! Especially if the UPS has a 5v dc output.
