As you seem keen to avoid any sort of regulation, all you need do is google "Ofsted no requirement to register " and you’ll find the list. I’m quite surprised you’ve not yet done this; even more surprised you think MN is the place to engage in business start-up research.
Your tax situation will become more complicated as you will need to account for being both employed and self-employed. If you figure how to do this yourself it will only take a few hours each month to keep records and submit annual returns. A low-cost accountant can probably do it from £250+.
Assuming teaching already puts you into the income tax-paying bracket, you pay £2 of every £10 taken in income tax. Additional national insurance payments for self-employment will I think take another £1 in every £10.
HMRC (never know for their generosity) estimate wear and tear as a 10% expenses allowance in childcare. So, as a conservative estimate, take off a further £1 in every £10. You now have £6 left from the £10 daily charge, before any other expenses.
You can get public liability insurance for this sort of 'club' scheme, but the cost will be inflated by your lack of Ofsted registration and because you’re not using a publicly licensed venue. You will also need to change your home and contents policy, to allow you to use your home for business purposes: the annual premium will significantly.
You’ll need full safety and fire protection and defence equipment: main linked alarms, CO monitors, fire blanket, extinguisher, etc.
You should make physical adaptations to your property in order to be accessible to potential users with mobility issues, to comply with the Equality Act.
Because you won’t be a registered childminder, you may need planning permission forchange of use of your premises. This costs £hundreds in terms of money, time and legal fees. It can be blocked by one neighbour's object or an existing covenant in your property deeds.
If you don’t already have a first aid certificate, training will cost around £90 and take one weekend every 2 years. You’ll probably need a level 2 food hygiene to register as a food business (just to store packed lunches and serve juice and snacks) and be subject to EHO inspection at any time: difficult if you have to take a day off work for any of this.
That’s all before you’ve spent a penny on advertising, toys, resources, craft materials, or whatever the club is meant to be doing.
The paperwork won’t be as onerous as the learning records required for the early years. It’s just a few hours on due diligence, taking and keeping child details updated, safety checks, recruiting, etc.