To think someone MUST be profiting from private nurseries?

To be honest they are not a public service .. you choose to use it so .maybe pick a fight with the government .

Why don't you ask them? Would save you an awful lot of speculation and satisfy your curiosity.
Of course, go with all the facts, such as how much they pay their staff (rather than assuming), how much they pay per month for rent, utilities, insurance, checks, training, equipment, food, etc, and have that total set against income from parents/govt.
Then you can really tell them what's what about running a nursery and profiteering from it

Most nurseries will be part of a limited company.

Look them up on companies house and look at their accounts.

If they are small they may only have a balance sheet but there are giveaways.

Look at - movement in profit/loss reserve year on year.
Payments to directors/directors loan accounts
Amount of tax paid
Cash at bank (although be careful, holding cash doesn't mean profit)

These can give a ssnse of scale of what's being made.

I've often wondered about just how much money nurseries make. Given how much they charge and how little they pay their staff I always come to the conclusion that it must be loads

There's a reason private equity providers have backed some of the chains - There's absolutely money being made.

1. the buildings. Rental charges etc
2. service fees charged for things like marketing materials, access to any IT systems, financial services.
3. use of young staff & trainees who are paid lower minimum wages

There are other areas i won't go into here.

This government love large nurseries because they don't understand, childcare provision is something you cannot scale up easily to reduce cost. The biggest costs of caring for children are the staff & the premises, and ratios mean you can't reduce the staff. Scaling up actually adds complexity and creates a need for extra costs for marketing, finance support etc.

If the government truly wanted childcare to be cheaper, they'd be on a huge campaign to encourage childminding, which is a much lower cost model as people do it from their own home using toys/equipment they often already own.

The birth rate has fallen markedly over the last 15 years. Childcare demand should have reduced, not risen, yet in most areas there are not enough places

The nursery we used was definitely making a profit due to the cars the owners drove, and why would they do it otherwise. £73 a day is insane, it was around £45 a day when mine were little. Back then the other parents who used nurseries were working parents as that was before the government started offering free hours for younger kids. I can understand why some parents try and work from home with young kids around when it’s £73 a day, though I don’t agree with it.

The government aren't paying enough for those free hours is my understanding. So they make a loss on what they give. But being a business they just charge the parents that loss. It's more the independents that will struggle I think.

Back when DD went to nursery they said the same and then the company (group of nurseries, Kiddi Caru) posted saying they made 11 million profit. Didn't quite fit the narrative. That was 12 years ago.

Also, why not have a discussion about profit with a nursery owner? Get the facts rather than make assumptions?
I am sure they will be delighted to discuss your finances too

They are businesses, if they weren’t making a big old profit, they would not be running. They are like dentists, always pleading poverty … but making a mint.

Well they are not a charity

Of course they are struggling, they are driving 2 y-o porsches