We're talking just about the small area around the corner of Kirkdale and Dartmouth Road, so going from The Foxes up the hill and round to The Bricklayer's Arms, with a bit up the hill toward the Kirkdale Institute - i.e. this http://maps.google.co.uk/maps?f=q&sourc ... 3&t=h&z=18
So it's not 'Kirkdale' in either the sense of the bit by the station where the Kirkdale Bookshop is, since these are separated by some residential in-fill, or in the sense of the part at the top of the hill. This small area does feel like its own small centre, and of course was, historically the old Sydenham High Street - hence its Grade II listed 'High Street Buildings'.
We could debate what might be a suitable name for the area till the cows come home - hope that turn of phrase is not too rural and villagey here - but it's perfectly possible for an area in a big city to be called something Village - it may now be fairly chi-chi, but Greenwich Village seemed to get by without a quaint old village green

And if the traders up there can get on and work together to promote their little bit of Sydenham, maybe by this very fact they've found a little bit of village spirit, and can call themselves 'Kirkdale Village' if they want to, and if they stick at it, the name might stick.