HOP here, though I'm another "halfway up the hill" case, but more like three quarters.

The post office definitely thinks I'm Forest Hill in all those automatic find your address from the postcode things and I keep changing it to Honor Oak.

However, there's also a fine distinction between Honor Oak and Honor Oak Park. I'd welcome a discussion on exactly what the difference is, but I always say Honor Oak, without the Park. However, one wouldn't want to be confused with the Honor Oak Estate, which is halfway to Nunhead!