I find the dulwich area a bit incomprehensible, price-wise. It's lovely, but oh so twee yet surrounded by some of the s* bits of London. But maybe that's just me :)
Also, I can't believe that people paying £1m + for a house would be concerned about state schooling options. Surely if you can afford a house that big, then you could extend yourselves to private school fees?!?!?!? Of course they could be principled sorts who just want to go the state option.
And none of that answers your original question, sorry!
I am not particularly fussed about what a house looks like from outside, or period features. Location and internal/ external space are key for me. I would choose ultra-modern if I had a free choice tho. So 1, 2 or 3 would all be goers for me if they were right in other respects.
I do not really understand the obsession with 'period' properties at all. Victorian houses were notoriously poorly built and often need loads spent on upkeep and running repairs. Think broken sash windows, damp, etc etc etc. Also, IMHO they are often darkish, necessitating all sorts of fancy side return/ light-well type modifications. I just don't get it. Any house can be 'period' - I particularly like 60s and 70s built architect-designed houses like Span houses and similar. They were built with a careful eye on how you actually used living spaces IMHO.