I just read the OP, I think you've answered your own question, children shouldn't be about potential monetary value. It's up to parents, playing this whole adulting game, to either look at current income and expenditure, plus look at how much raising your 2 children has cost, if you cannot afford it, which I struggle to believe for reasons I will move onto, then you need to abandon the plans and get contraception. That's if you really, really, really, can't afford it.
I state a bit of disbelief because tax credits are new, new in my lifetime as an adult, yes I'm no spring chicken. So in the past parents had to get by with very little support. I know there will be those who bark, this isn't the past though!
My great grandmother had 12 children, in a 3 bed house, although given the age gap between the youngest and eldest, there wouldn't have always been 14 people living in the property. The trend pretty much continued with large families, apart from my generation and the one below who either chose not to, or couldn't if they wanted to.
In our household the income isn't anything amazing, but we don't qualify for tax credits. We still get child benefit. We don't live an excessive lifestyle, we have the same bills as most families.
I'm guessing if you have 2 DC and after the second, you thought I don't really want to end it here, you kept some clothes. You know for the first year, you pretty much get away with not having to dress baby, apart from a coat and extra layers if going out. Hopefully you have clothes, or know someone happy to give away clothes. If not and you were in super dire need, I'm sure someone on MN would donate vests etc from their DC.
There's the option of breast feeding, if not viable formula feeding, I am pretty sure that due to the tax credits you will get healthy start vouchers in pregnancy. So that can help towards formula. The HV told us Aptamil was made by the same people as Cow & Gate, we made the change no problem. If your baby needed special feeds, you would get those on prescription.
So we've covered clothing & feeding. Ok nappies, people rave about supermarket brands, it's trial and error. Water is the best thing to clean babies bottom with, no need for wet wipes, although with 2 DC I expect you always have some handy. Pushchair, I'd honestly give baby wearing a go if viable. Sleeping, I'm sure you could go to a shop that specialises in households on low income, so you could possibly get a cot & mattress for free or very small contribution. That's if you don't still have the old cot.
Hopefully your relatives will ask if you need anything, so the basic needs of a baby could be met by relatives, instead of a fancy outfit ask for vests and the staples you need.
Child tax credits are for children, I believe it's circa £65 per child, then you get the working tax credits that top that up. I believe there is a child element to working tax credits so whatever that is, add it on. So I'm sure splitting it 3 ways instead of 2 won't be that tragic. My emphasis is on child they're for the children's needs - so gas, electric, water, council tax, TV license, you would have to pay regardless of whether you had children or not.
You really need to think if you can afford this extra child, remember the best things in life are free, you don't need to pay for days out, you could save for a special trip now and then. Play parks, nature reserves, reservoirs, canals, all free to walk down/around/use. If you honestly can't afford it then you need to take action. I believe you could afford it, my parents had a mortgage and 6 children, although my Mum worked part time when Dad was at home for her own spending money. But my Dad's wage was minimum wage as was my Mum's.
You also need to think whilst you feel hard done by the government are short changing you, this is the reason they have put the cap on, as it should promote posts like this, where adults think, can we afford a baby without the government subsidising it. I also know my sister has one child via IVF, by brother is going through IVF. For both of them it will take a miracle to get baby 2, in fact it will take a miracle for my brother to have 1 baby. There are those who are reading this, or simply read the OP and died a bit inside, because they simply would love 1 child. So if you can conceive relatively easily, you should count your blessings.
This isn't typed in a rangy way, but advisory way.
I will read the rest of the posts and see what others have said. I may have duplicated what others have said, but I'm sure if you looked at your budget, you could skim some money somewhere to make it viable. I guess realistically there's little point in you trying to work as it would affect the tax credits you receive, so also feel blessed you get quite a lot already from tax credits, which affords you to be a SAHM. It's not a luxury everyone has.
Good luck to you, I hope you can make it work, so you can achieve what you want. This is probably a time in your life you look at outgoings and think, do we sacrifice this and have a baby, or is this more important. Remember most of the best things in life are free. Check to see if you can lower bills on comparison sites, also see if adding you or your OH to each other's car insurance brings it down.