I have to tell you that I was in your boat a few months ago. My family is that of only 4 (5 and 18 month old) but our situations are incredibly similar...from Jersey, moving/ed to London, generous housing allowance, our children's private schooling is paid for (hopefully yours is?), etc. We're considerably lucky.
We wanted Notting Hill too but found that it was just not worth it. It's a lot of hype for not a lot IMO. While I loved the idea of telling folks back in the states "Ah yes, we live in Notting Hill", I didn't love the space it would give us for what we were going to have to pay per week. In order to get what I needed to feel semi-normal I would have had to pay between 3,000 and 6,000 pds. per week. Seriously...and that is simply not in the definition of "generous housing allowance"...that is astronomical and ludicrous (BUT, I certainly wouldn't be turning it down if it were ever offered!). If you're in that type of boat...more power to you and enjoy Notting Hill.
We however live quite decently but in Zone 2...it's about 1600 square feet, 3 bedroom, 2 reception room, eat in kitchen, garage and garden, with off street parking...Belsize Park. My rent per week less than 1000 per week. It's right in the middle of everything I need and is close enough to my daughters private school which is in St. John's Wood. The tube is a 5 minute walk, shopping is close, the busses are close, the park is close, Starbucks is down the street (though their coffee is terrible), the Swiss Cottage new state-of-the-art Leisure Center (i.e. Athletic Club/Gym) is a 5 minute walk and the library is right there too...I have yet to need a car other than my inherent need to have keys in my pocket, a place to keep the damn stroller and a means to get to CostCo. Primrose Hill is close enough (with a FAB park) and I don't have to pay their rent yet can enjoy their high street. It's lovely and it's big enough. Oh, and I can walk for another 15 minutes up the hill and have Hampstead's High Street. Perfect house? Not by any stretch...looks totally like I'm living in the projects but considering what I get with it and how well done it is inside? It ROCKS and there really isn't anywhere else I'd rather be at this point. Steeles Road maybe but that's just for a look at Jude Law while he's popping in to say Hi to Sadie Frost!

We moved from Jersey last month...Westfield area and my husbands commute into NYC was 1.5 hours on a GOOD day. One of our necessities when we moved here was that his commute was 45 minutes or less. His commute is now 30 minutes...he doesn't work at Canary Warf though but instead at London Wall. I'm not sure what the commute would be like to the warf from here. Regardless, NW3 is definitely something to consider and the commute time is good to have as one of your preferences. It makes a HUGE difference to have him home at 6:30 instead of 8:30pm.
PM me if you want to chat more about places...since we just went through it, maybe I can offer some other suggestions without boring everyone else with my jabbering:) Good luck...it's quite a lot of work but oh so worth it!!