It sounds like OP has a couple of different issues -
She can’t get home in time from the office collect DC from nursery before it closes.
There is no after school wrap around care.
I’m assuming she may also have the more immediate problem of it currently being school holidays.
Financially she will be worse off.
Some of these are easier to solve than others.
How much earlier than 5pm would you need to leave work to be back in time for nursery pick up? 30 minutes? An hour? There is case law for indirect sex discrimination on employers not allowing women to amend their working hours in order to collect children from nursery. If you requested to reduce/amend your hour and they denied this you would likely do well at tribunal on this. Note they do not have to keep pay the same. If you have to leave an hour early they could pay you an hour less and not allow an arrangement where you get paid the same. But the point is there should be a way around this one where you get to still have a job and can pick up your child.
After school wrap around care - the school might not provide it but there might be other organisations like after school clubs or childminders that do. Hopefully you can find something before term starts again.
If you have a more immediate school holiday issue I don’t know how you solve that one, so many holiday clubs don’t cover a full working day. University Nurserys often run them that cover a full day. Some may have spaces but that’s another £45 a day easily gone. If you’d have put a plan in place with your employer in advance then it would have been easier. But also I’m making assumptions, maybe you have the holidays all worked out.
Financially I’d probably do what I could to manage with the extra costs now whilst I looked for a different role. I assume you’re better off with this job than without out? Don’t jump ship without having one to go to.
Thinking about Nursery. If you wanted to change nurseries (I appreciate that’s a big thing) then you’d need to start in September for the free hours to work. So if you need to give your current nursery a months notice than you need to sort that asap before we get to August.
I’m sorry OP the juggle is really hard.
Personally I become self employed because I got fed up with all the corporate crap that just put barriers in the way of me getting to do the job I want to do and trained very hard for but I’m lucky I have a job where I can do that. I work from home all the time, DC have childcare 3 days a week and if I need to work more I do it at the weekend so DH can look after the kids. Some weeks I work 5 days, some weeks 3, some weeks less, it depends on the demand/what else is on.