What they cost as infants is nothing compared to the impact of loss of income due to statutory maternity pay (unless you have amazing enhanced benefits at work).
Babies - big expenses are a car seat, pram, cot. Most other things you can get second hand or very cheap eg high chair, sling/carrier, clothes, toys. Nappies are expensive but I found it offset the cost of me being teetotal while I was breast feeding.
If you can find a funded nursery place you will be lucky but it isn’t free, so your research and your budgeting. Nursery was ruinously expensive when my kids were young and I didn’t make a profit from working (but needed to keep a foothold in my career), I spent it all on childcare (although I did at least get a pension contribution). I really hope the government sorts out the mess it has made of subsidised childcare as it would be a game changer.
Toddlers are otherwise very cheap - don’t need a seat on planes and can share a room with you on holiday. They are just as happy playing with a cardboard box as the whilst tech toy you invested in.
As they get bigger you’ll have to pay for a bed and a larger car seat, I think those have been our biggest expense. Sometimes you can get kids beds second hand (just buy a new mattress).
At school the costs rise - school uniforms are available second hand but you need to fork out for trips, water bottles and lunchboxes, school shoes that are destroyed somehow on a regular basis. If you’re working you’ll have to pay for Holiday Clubs (I budget £30 to £40 a day) and probably Breakfast/After school clubs. And you’ll end up paying for activities and hobbies - say £25 a week. Oh and of course, birthday parties - both hosting and attending. That can get a bit costly.
I buy most of my kids’ clothes on Vinted - including coats - but not trainers/shoes (although have bought wellies, sandals and boots as these don’t get much wear, typically).
Teenagers are expensive. There’s the trips
and school supplies and established hobbies to pay for. They eat loads. They want expensive phones and trainers (you can obviously say No.) They want a Spotify subscription and an epic bedroom makeover and pocket money which they won’t spend wisely. And they start needing a separate room on holiday. And then school insists they have a laptop and no, a Chromebook won’t do. And then driving lessons. But you can make them get A JOB and then it’s their problem. Until university when your income means they don’t get a full student loan and you have to top them up.
Basically: save up.