Don't overlook the advantage of being outside of London for so many other things that come with family life and critically, right now, the ability to get more bedrooms for your money which would allow you to bring in a live in nanny.
However, that is not as straightforward as it seems !
I moved out of London after living in my house in Angel. I was in the City and later the docklands and I could not understand why anyone would live outside Zone 1 or Zone 2 at a push. Richmond possibly, but the trains were awful and tubes worse.
Other places came along and "became gentrified" and highly sought after despite awful transport simply because they had good schools and options for bigger houses for your money (back then).
Childcare when toddlers is only the start of it. If your local state school is awash with all manner of lower end immigration then your child's future will be curtailed unless you pay for a private school. That will make your £50k a year on childcare look like a charity event. £30k a year each is ballpark after junior and more if you want boarding, which you will discount totally now but revisit in your thoughts many times over the years.
When you move out of London, your London house money can buy a far better place and whilst you may be taking a one way trip in terms of house prices, you won't want to move back anyway.
The downside is that commuting can mean a first class train ticket and train station car parking, often necessitating another car purchase. My commute was an hour and first class was about £8k a year and parking another £1500 or so. If you opted for standard class then you may not get a seat and on some trains they have gone to 3+2 in the the Ryanair of train services so you are squashed all the way to work.
But you can get your child into one of the country's best state schools for free and that stays free until 16/18. Otherwise you are going to be ploughing the best part of £100k a year into schooling and perhaps not getting very much back from it.
I would weigh up the options. Saved school fees, live in nanny, larger house, versus a longer commute (often easier and you do get your "commuter legs" after a while). A nice 50 minutes into London on the train can be a nap, some work or just reading the paper. It is quite ok actually.
Inside London, unless you can afford the larger house and the live in nanny, then you are permanently compromised. It is hard to consider getting out but until you write down the numbers, now and for the future, it won't make sense.
What should make sense is that you should be able to retire 5 to 10 years earlier if you live outside London and don't have the private school fees.