It's been inadequately funded ever since it was first introduced in 1998. You've presumably only just noticed now because this is the year that it affects you, but it's not going to magically become adequately funded. It's fine to "make a fuss" by e.g. writing to your MP and demanding that the government increase the rates paid to nurseries to something reasonable, just don't blame the nurseries or try to wriggle out of paying it. Someone has to pay the cost of the service you want, and the government won't.
They way that some nurseries manage it for free is:
minimal spending on furniture, decoration and flooring
minimal spending on resources, toys, consumables like paint, paper etc
minimal flexibility - e.g. if you only open 30 hours per week term-time-only
work right at the boundary of minimum amount of staff to children ratio so that there's no spare pairs of hands when things get chaotic
If operating on Council-owned premises or within a school building, the nursey may have no rent/utilities bills to pay and may be taxed differently which would affect the balance sheet.
If you want to send your child to the lovely nursery with the nice well-maintained garden, and lots of lovely resources and a weekly range of activities which keep your child stimulated and engaged, and which tries to have a better-than-minimum staff-to-child ratio, and which is open for longer than 30 hours per week and in the school holidays too - that all has an intrinsic operating cost which works through as an hourly cost of care which is typically 20%-40% higher than the amount that the nursery receives from the Government. Without top-ups, the nurseries would go bust. It will get worse once 30 hours for all children over 9 months is rolled out.
You are right that it's the same with breakfast clubs. A lot of schools are opting out of offering them because the amount that is offered is woefully inadequate for the costs that would be incurred, and that initiative has been structured so as to make it pretty much impossible for schools to charge any kind of top-up, so they just can't do it.