We lived in NW1, W1H and SW1 for fifteen years and it was totally doable with two earners even starting on a perm salary of 35K, and as the income increased we stayed, but within three years of kids arriving, it was clear that we needed to make a choice. Stay with a two-bedroom in Zone 1 - and pollution etc - or jet to Zone 4 and triple our space.
Five years later I think it's more feasible to stay in Zone 1 or 2 with kids as the air becomes cleaner and you should have saved up enough to find a bigger place. A friend travels from Zone 1 to 4 every on the train for the school run, so it's perfectly doable given flexible working.