Those are parishes, no?

You're right, that map specifically shows parish boundaries, useful and interesting historically as they were used as the basis for administrative areas. However, less useful in the 21st century as their only purpose, as far as I can make out, is to tell you which Anglican church you should worship in.

Ha ha, I onced had exactly the same problem! I thought it was going to be quite easy to solve, but it took a fair bit of research in the end. Steve G has briefly addressed it. I'll try and explain it in more detail...

Present

Borough Ward
Postcode
Parish

Past

Parish

Each of the above systems have different boundaries--both past and present. Even parish boundaries are not the same as what they used to be.

I've provided a map of current Parish boundaries, but you may decide to base where you live on Borough Wards or Postcode boundaries. The boundary of Lewisham Parish dates back to Saxon times, and we used to have to pay tithes to the church, so I prefer to use the Parish system. Again, it's up to you which system you use, as long as you use one of them! Catford Road has never been known as Forest Hill at any time under any system, but Ravensbourne Park is now in Forest Hill--only under the modern day parish system. The whole of Forest Hill and Sydenham can be described as Lewisham to your friends, if you like, based on the ancient parish system.

An historian, I believe, needs to incorporate all boundaries/systems from different times if he is to effectively cover the entire area known as Forest Hill--past and pressent.

Damn, I need a cup of tea already... This subject is so complicated! Local history books often fail to address boundaries, and I can see why, but then it enables one to understand where they live in context and perfect harmony. Right, I won't bother correcting my spelling and grammer; I need to put the kettle on sharpish... --Falkor (*exhausted*)