It probably will cause upset to challenge this because it's a situation that's benefiting him at the cost of his partner and child.
However, it's so worth doing.
I'm writing this assuming there's no issues with whether he wanted the child, and that you are not in an abusive relationship (although I'd honestly say what you are experiencing is unfair and that you're worried about raising this makes me question whether this is part of a larger pattern of control?).
You need a budget. Start adding up the household bills. Use a budget template such as provided by money advice service and money saving expert. Have this info on hand when you talk to him. You need to explain that the current situation is unsustainable. The carrot is that by dividing your responsibilities more fairly and working together, you can improve your family finances and plan for stuff you both want to do. Right now he is living with a partner who is unhappy and struggling. He could help to make this situation better, for all of you. (This is actually the bit I find so stupid about his behaviour - he is actually making his own life more difficult). Each of you has more than a financial contribution to help the household run. Right now, you're caring for your child. That is your contribution. If you paid someone else to do it, it would cost a lot more than it would for him to support you.
The classic way to work out a bill split, if you're not comfortable with a joint family budget, is to work out your total household income is and how much each of your incomes are as a percentage of that. Then look at how much your total monthly bills and food are. Each of you should be contributing to that in the same percentage as your household income.
So say your monthly incomings are £3k, for the sake of easy maths. You contribute £1k and he contributes £2k. You contribute 33% of household income, he contributes 66%. Say your bills are £2k a month (again, give me easy maths!). He would put in £1320, you would put in £660. It's still slightly unfair as he would end up with more disposable income than you but it might be a start as you move towards more equitable family budget. If you are able to joint budget it means you can pool resources to save for things like holidays, refurbs, retirement etc etc . But I wouldn't start with a joint budget right away as there's clearly some other issues going on.
Still, there's a possible way for you to illustrate to him why your current arrangement is not sustainable. You are currently probably contributing 100% of your income or more to living expenses. Your savings should not count as income in this scenario.