OK I have a go at this as well.
FT nursery is what about £1000 a month ? And some of this often tax deductible so let's go with £800 + say £100 for nappies, extra food and clothes so £900.
I am going to take a 14yo as an example.
Clothes
Dd needs: school shoes (adult sizes, likely £60-80 twice a year), then trainers for P.E (£60), something to wear on her feet at the weekend (be lucky to get it for less than £80) these all need replacing 6 monthly. School blazer can be £100,uniform skirts are £45 and she will need 2, the blouses are £15 each and really we want 5, school jumper (I got 2 another £25 each. Then P.E kit (hoodie £45, I bought 2 in case of loss/ laundry crisis, culottes £25 and polo shirt £25X 2, tack suit bottoms £20). She needs hockey boots for just 1 term,so that's another £50). Remember growing girls need proper bras last time I checked they are best part of £20- she'll need at least 3, at 14 you are likely need to replace these at least once, maybe twice a year. Under wear obviously and tights, which regularly get holes/ladders so I'd be buying a packet most weeks in the winter (£20 pm). Sports socks in regulation colours which get lost almost weekly £9 a throw and white socks for the summer uniform. Oh yes 2 summer dresses (£65 each).
At 14 Dd need women's clothes and as an absolute minimum needs 2 X winter casual bottoms (trackies or jeans), 2 warm tops (hoodie or similar) and 7 or 8 tops. She will also need something to wear to a party and possibly shoes to go with (she won't want to wear her school shoes) total £200. This wardrobe will be outgrown in 6 months. In the summer she will need a swim suit (again I got 2) and sliders this is at least is cheap possibly all in for £60. Really she needs casual socks as neither of us want her wearing her school socks " out" so that's another £10 2 or 3 times a year.
Essential equipment
She needs a school bag obviously and stationary (parents are often expected to buy "set texts") a bells and whistles calculator (£35) which may not last the year. My experience this about £50 a month. You could I suppose not get them a mobile phone, but most do and a " basic" package is about £20 a month (again assuming no breakages/losses, which not a given). Then there is equipment for things like D of E/ field trips. Remember they are growing quickly so for example a sleeping bag which was OK in yr7 is likely out grown by now, they may also need specialist clothing (and/ or shoes ££)
Transport
You might be lucky and get a free bus pass but often not and they need to be able to get from A to B specially as you are working, you may need to pay for odd taxi this easily coss £75 pm.
Personal items
OK you could make your 14yo daughter wash with plain soap and wear no make up. But a reasonable budget for cosmetics might be £10-15 a month. It is unlikely they will be happy without a professional hair cut every 3 months (£50) but I suppose you could try. They certainly need to be provided with sanitary products and hair removal equipment (I'd want my daughter to have what she wanted/ needed in this reguard) this probably add £5 a week to my shopping.
Food
School lunches are £20 a week assuming no free school meals and I think another £10 for snacks/drinks out of the home is reasonable given they are making independent journeys. ONS suggests the cost of feeding a teenage girl is £42 so let's take that total £72 pw.
Activities
OK let's take the school ones first, a trip to Yepes in Belgium for history is £150, Thorpe park with the school was £45, not counting things like skiing or theatre to see GSCE texts. Let's say £50 pm
Then extra curricular again parents are working ft or even if not it is likely you want your 14yo to do something outside of school, these are generally an average of £150 a term (this is how much a "bog standard football or swimming club costs, dancing or riding is obviously much more). Ditto musical instruments.
Finally independent socialising again you could say no, but personally I think going to the pictures with your mates on a Friday night is something I want my 14y to do-£20 after popcorn/McDs etc.
This doesn't include spotify/ Netflix which many people would consider essential.
Now tell me that adds up to less than FT nursery with your child care vouchers.