I think it's a complex issue.
On the one hand, most people need two full time incomes to afford a house large enough to have children. So with most parents, both partners will work full time. And on the other hand, long term as a society we do need people to keep having children. So therefore, some kind of (properly) subsidised childcare makes sense.
On the other hand, there is an element of individual choice to having kids (and certainly how many), and have both parents working full time. It is unfair to ask young single people, or older childless people to subsidise what is partially a choice.
And as people have said, when you get to school age, there's still wrap around care, holiday childcare etc to pay for. For many families it does make sense for e.g. both parents to work 4 days part time/compressed hours, or one or both to work term time only, or to have a parent working flexible hours/shifts etc to bring the childcare bill down. But I fully accept for some families this isn't possible, and I do wonder if certain jobs (e.g. healthcare) should come with subsidised childcare. For private sector employers, perhaps it's on larger employers to offer heavily subsidised childcare as a benefit?
Part of the issue is definitely that wages have not kept up with house prices- it isn't so long ago that families where both parents worked full time weren't the norm, even in London. And there's no reason it has to be the woman who works part time, either.
I do feel for nurseries (although I accept that there are ways and means of communicating it to parents). They are dealing with rising costs (rising staffing costs, higher energy bills, higher costs of consumables, probably increasing rents etc), whilst parents are expecting their bills to come down by a significant amount, and there's no way to make that work.
I can totally understand why parents feel annoyed too. However, I think the overall issue is part of the wider cost of living crisis.