If you are seriously considering having a child with him, I think you need to thing through the ramifications for you.
Firstly, can he contribute equally to your life. Secondly, how would this work in terms of where your joint child would go to school. Could he fund his son AND any other child going private. And if he couldn't, how is he going to justify that - not to you - but to this child. And potentially even to your children as their step dad as it could very much make them feel 'lesser'. How will he handle them potentially having to make sacrifices like family holidays, in order to fund their step sibling's education at no benefit to themselves? And that makes it a fair question to be putting to him.
If the answer he gives, isn't to your liking you need to reassess where you go from here. Is having a child with him a good idea? Do you want the financial burden as a household to support the luxury of private school? And if you don't, are you willing to walk away from the relationship rather than go through the years of resentment you have.
Ultimately I think this is a crunch point in your relationship where you need to decide just how serious you BOTH are about each other and whether you think you can work together, be on the same page about crucial financial decisions that impact your life together and whether you have the same priorities in life.
Given his income and the maintaince he will already have to pay, I do think he needs something of a reality check. If he is in a relationship with you, he has a responsibility to you and to your kids. This is probably lesser than to his own child who should come first - how far that goes and whether thats at the direct expense of your family unit should be up for debate though. Its not the type of decision he can make alone as a result.
Ultimately its for him to make decisions about his son's education alone, but its not for him to make big financial decisions alone. If he does make that decision alone, I think you need to reassess where that leaves you and your kids in the long term.