This!^
OP, childcare is shit, and it should be more affordable as it's shitty for women in particular. BUT, come on. You have a household income of presumably well over 100k. You do realise that the average household income in the UK is 32k? AND that is the AVERAGE. Working single mums, for example, may well earn 20k, for example. Even in London, you cannot seriously plead poverty.
Do you go on holidays? Do you buy clothes? Do you save? Do you HAVE savings? Is the only reason you don't have a car because you live in London, where it isn't needed? Do your children share a room? Do you have spare bedrooms/bathrooms? Do you ever go out for meals? Day trips? Nights out? Do you have a computer? Decent mobile phones and contracts? Do your kids get new toys? If you answered yes to any of these questions then, sorry, but you don't get to plead poverty!
My goodness. You do realise that many, many families are working poor? People need to work, but their wage barely covers their food and rent. Childcare is more than their rent, but if they can't get childcare, they can't work.
I've personally been in this situation. I've been unable to buy essentials like clothes and food even while working. I haven't been on holiday in years. My computer is 8 years old and ready to kick the bucket any day. My kid has charity shop clothes, and even then sometimes I can't afford it.
I actually have a fairly good job - I have a degree and a postgraduate qualification, and I am in a promoted post in my field. But I have a chronically ill spouse and a child. It doesn't cover us all. I work two jobs. I work really, really hard. I've been successful. I've been resilient. Sometimes, life just throws you a hand, though. Free places are there for people like me, as they should be, so that my family don't need to be on welfare.
So, yes, your post sounds whiny and a bit entitled. If you go on holidays then don't go on holidays until your kids are old enough for school (join the no-holiday club, but at least you'll get to go on them someday). If they don't share a room then downsize so they do (again, join the club, but at least you'll be able to upsize again one day). Do you go out for the occasional meal/day trip/night out? Yes? Well, join the 'going without club'. Do your kids get new toys? Well, join the shitty 'you've got dusty, semi-broken second-hand gifts' club.
Seriously, stop moaning. Yes, childcare is SHITTY, but your life and income is fine. Do what everyone else has to do and sacrifice for a few years. Suck it up.