I pay "only" 10% more than the exchange rate adjusted amount you're paying. Top 5 US city. Don't take too much stock in the ridiculous numbers you hear. I've lived in podunc land, the suburbs, and major city and I always paid within 10% of what you're paying.

£1200 in my top 5 city would get you a newly built daycare, with all the modern gizmos, a kitchen built "especially for young children", a teacher with 10+ yr experience, and peer children who are the son/daughters of doctors and lawyers. ~£800 gets you an average daycare that is fully up to license / code and generally does a decent job. ~£600 will get you a caring but gray market (usually bilingual or limited english) stay at home mom with a home daycare business.

I would wager the vast vast majority are paying close to ~£800, either through the black/gray market with unlicensed caregivers or in licensed facilities in the vast majority of lower cost of living portions of America.

How many hours a week/day?

And yes, it's likely subsidized; around here there's "free 4k" and some of the pre-4k daycares are subsidized in various ways.

government subsidized?