I’m not suggesting he doesn’t have faults, and personally I wouldn’t be with someone who would be petty enough to use my child in any kind of argument because he lives/eats/bathes there- BUT in general terms, OP & him are not at all functioning as a family unit financially, they are still just like room mates really, or rather DP is like a lodger. As evidenced by the fact OP has said she pays for days out, she pays for nappies, household things etc. There is a much much bigger conversation to be had here about finances in my opinion.
You are a family, you’re living together, share a child, thinking of marriage- at that point you really need to be sitting together and sorting finances out first. It shouldn’t be you paying for everything and him just making a set contribution of £500, you need to be sitting and even just go over your statements for a month and write down every single nappy, tub of formula, pack of wipes, toilet roll, toothpaste, kitchen toll, muslin, blanket, loaf of bread- EVERYTHING and see how much that comes to in a month. He shouldn’t just be giving you £500 of his wages towards ALL of that plus rent etc, you should be sharing these costs much more than you are because I’m positive that £500 does not even cover a third of what you are currently spending.
He is not wrong in saying that for most married couples, regardless of your individual set ups, money IS “family money”. If you’re not going to combine money and you don’t trust him to do that, then as a minimum you do need to be sitting down and having a proper conversation about how your finances as a unit look. Show him what it would look like to ACTUALLY be “sharing” the family costs by using a different method of “sharing” rather than one big pot.