I think we can all see what is actually happening here but no one wants to be the one to say it.
OP had her own romanticised plan, albeit a shit plan, and what she thought was going to be, as PP said a "life of luxury" banking on someone she barely knew suddenly falling over to fund her, appease her, and give her the right to remain in the UK, all because she got pregnant as fast as she could.
Turns out this guy was somewhat unaware of this plan, probably made some noises about "yeah kids great" in the moment in order to get a shag, not for a moment meaning to ever have a kid with OP. OP purports this as he wanted to seriously start a family, hence the immediate pregnancy can be "explained" for another reason than the rather obvious elephant in the room.
He's then got pregnant OP, who he's housing, paying all her bills, while her VISA prevents her from working only whilst pregnant (sorry, what??). The child is here and now he pays for everything and for the kid to go nursery 3 days a week. OP doesn't fancy a job, and on top of all her housing and bills paid, gets hundreds of pounds for "fun money" a month. Consistently asking for more because she spends it in the first two weeks. Except turns out she's been pretending to spend it and banking it in her own private account, then asking for more. Wonder why he's pissed off.
OP you need to wise up. Because you aren't even entitled to anything you're getting at the moment. Let alone asking for more. You're not going to be a kept woman who lunches, just because you think you should be. That's not what having a kid entitles you too. You clearly had that expectation with all the "thought he'd change when the baby arrived." You've got a very good "deal" at the moment compared to what you are both entitled to, and bringing to the table in this unmarried situationship.
Sorry to tell you that if you want more money than you are voluntarily being gifted every month, you need to get off your arse and get a job. Remember whilst it may have been your vision, his plan wasn't ever a position where you were living off him. Just because he's tolerating it for now, does not mean he won't get sick of it equally quickly. And he owes you nothing but child support. Which if he owns his own company, and thinks you've "had enough out of him already" he will tailor with his income so you get very little.
Now you actually do need a plan OP. You have no income, no entitlements, no home. What will you do if he wakes up tomorrow and declares he's done and you're leaving. Because there is zero stopping that from happening, and all you seem to be focussed on is not having enough money for lunches out on the days you wander about with your child.
Seriously, what are you going to do?