Hello, late to this thread, sorry. From my experience (and I am a norf Landanaaaah, so can't advise on south of the river - although Brixton is on the Victoria line - very handy for your husband's work...)
I lived in Stoke Newington for a few years and can vouch for the fact that it is mummy central (buggies and slings and crazily expensive baby boutiques a plenty!). It's pricey, though, and it's, urm, how can I put it? Real. And, urm, full of character. I quite liked it, though. Transport connections a bit crappy as no tube there (yet), but there are two tube stations within about a 15-20 min bus ride away with very fast links to Green Park. If you're looking to get into a little mum's network, you'll do it with great ease in Stokey. Quite a hotbed for lefties and lentil weavy types, but even if that's not your thing, it's generally a fairly friendly place.
Crouch End is incredibly baby friendly, too, as already mentioned. Lovely area, not as gritty as Stokey, but also very pricey and pathetic transport links. Ditto to Muswell Hill / Ally Pally.
I think Green Park tube is on several tube lines - if your husband is planning on getting the tube to work and/or you want to get out and about around London, it might be worth looking at areas on those tube lines. Also remember, some very far out areas have good tube links into central London (we're in lovely, leafy, 'is it really London?' Barnet and can get into central London via the Northern Line in under 40 mins).It's very family friendly up here and there are some great schools and billions of toddler groups.
Just quickly - also lived in West Hamp / Kilburn. Fabulously close to central London / transport links superb - and a real 'best of both worlds' (grimey old Kilburn High Rd for bargain shopping and proper pubs / West Hamp for trendy cafes and arty types). Very expensive area, though.
Sorry for waffling on, and if I've repeated what others have said.
p.s. Where in Brooklyn are you coming from (just being nosey! I am a born and bred Londoner, but a New York obssessive!)