Aww, I remember these days :) I was so convinced of my own frugalness and how babies don't need to cost anything and everything is a fun little challenge.
Well, yes. Babies indeed can be perfectly cost effective if you don't listen to the hype. I reckon I could do the whole first three years on about £200 a year assuming that I could breastfeed (since I did last time, it's likely). That's including half decent car seats and a bike or scooter for the toddler, but not including lack of earnings and the hidden costs ie higher bills.
School stuff is expensive. We are abroad and there is no uniform but it's still going to cost in the region of €2-300 for all the equipment and bag this year. And even if you home ed you don't escape costs because you will want to join groups, which often charge to cover their own costs, or you spend more on petrol/buses getting around, museum entrances etc, swimming, sports/music clubs. Then materials for at home, books, kits, craft stuff, outdoor toys/equipment, paper and pens.
I find the most surprising thing is just that everything has an extra cost. If you want to go out for the day you have to pay an extra ticket for the DC, not so bad if you drive as it doesn't cost any more to have an extra passenger (though you do need car seats and a big enough car to fit them all in depending on how many you have). You can't just pick up a drink for yourself at £1.50. You have to buy one for everyone so it becomes over a fiver. You stop for lunch, and a child's lunch adds another chunk on. This is every time you do anything, it's multiplied. Even if you just go out with your partner, you have to pay for a babysitter which can double or triple the cost of a night out AND you have to be back at a certain time so it's not even as relaxing!
Then the hidden ones - you need a larger house so your rent or mortgage and council tax is higher than it would otherwise be. Your bills are higher because you're doing more at home. Your appliances (and your car) wear out faster and you have to replace or repair them more often.
People stop giving you armfuls of clothes at some point. For some reason it's really easy to get hold of second hand baby and toddler clothes and less easy after about three or four years. Probably because they just utterly destroy clothes as they get older.
Shoes. HOLY SHIT, shoes. I have begun to despise all shoe manufacturers. I think they should just have a club where you can pay monthly and get X pairs of shoes every year.