I'm in a similar situation to you OP - 2 DDs (aged 10 & 11) and they seem to make friends with the richest children in their classes, every single time!
DD11 went for a sleepover at a friends last week and she sent me pics of them in their hot tub over looking the river at the end of their garden, then some of them kayaking and paddle boarding, they were allowed to order whatever pizza they liked from Dominos and then got to choose 2 movies on Sky pay per view! That would have eaten up my entire monthly "disposable income" (by which I mean food and petrol money!).
However, we have become known as THE place for sleepovers, we average 2 a month (I usually let both DDs have a friend over on the same night to avoid anyone feeling left out). I just get some pizzas from Sainsbury's for about £1.50 each, make some popcorn and let them make a den in the front room with as many duvets, pillows, cushions, airbeds and pillows as they can find! We live in a flat too, but there is a park 5 mins walk away which DDs are allowed to go to on their own (together though), they make sure they have a phone (with a tracker installed) so we can contact each other if need be and a deadline for being home and the kids all seem to really enjoy having a bit of freedom - I always check with their friends' parents first though!
A couple of other things we do; when the cinema does £5 tickets, I use a Meerkat Movies code and they get to bring a friend each - I let them have a pound each to buy a treat in Tesco rather than let them loose on the concession stand in the cinema though! We tend to go swimming every Sunday and it's only £2.75 each, so if I'm feeling "flush" (if payday has been in the last week!), I might let them invite a friend each.
My DM says my sister and I were the same, that she always felt intimidated collecting us from our friends 5 bedroom detached homes, when we lived in a tiny 2 bed maisonette, but she says it got easier as we got older and she realised their parents couldn't give a monkeys how much money we had, they just cared that their daughters had nice friends!
Anyway OP, you're not alone and it sounds like you're doing a grand job!