Underground travel with small children

I live in London and my experiences with my daughter on the London Underground have been disastrous.

The Underground is simply not Child Friendly.

The simplest of journeys involves battling with flights of stairs; no problem if you're a pedestrian, but a nightmare if you have a pushchair or buggy.
If you're on your own, forget it; you're going to be at the mercy of passers-by, and thankfully there are many who stop to help.

There are some 'flagship' stations which offer stair-less access to rail users. These are few and far between in Central London and tend to be situated in overground areas.
I can only imagine what the tube must be like for disabled users. Decades of under-funding have left the Underground an archaic rail network still stuck in the 1960's.