For what it's worth, the map in my head more or less corresponds with Michael's version. I've lived in Honor Oak for about 12 years and grew up down the road in pre-gentrification East Dulwich.

So I'd put Canonbie Road in Forest Hill Road. Just about. Cross Forest Hill Road and you'd be in Honor Oak. East Dulwich ends where the SE22 postcodes run out (Wood Vale?) so we can exclude that possibility. But I can see why the OP is puzzled because the road is close to the junction of three neighbourhoods.

Honor Oak Park is the 'official' name for the Honor Oak area but I never heard a local ever refer to it as anything other than Honor Oak.

(And I can officially confirm that residents might imagine somebody to be either an estate agent or a bit of a **** if they claimed to live in some mythical Narnia called 'Dulwich Borders'! Perish the thought indeed.)