I wouldn't say that flat is necessarily a problem, but I've found having a garden where I can kick the boys out to be invaluable for my sanity. Plus the cats might need plenty of spaces to escape- it's not necessarily so much about the cats hurting the kids, although that is a possibility, but the kids could also hurt the cat. Our cat was definitely the subject of a sustained campaign of attempted sneaky kicks and pinches if we stroked her in the kids presence at the start. We had to put a litter box in our bedroom anyway because we just banned them from going in there so that she could have some space in the daytime away from their screaming, shouting and attempts to love/cuddle/pull her tail. There were a fair few run ins before we all truly learned that cats are a lesson in consent.
On the other hand, I would say that if you moved now to a different area you might be asked to wait a bit to establish yourself in your new area and find your network though, so that's worth considering. Plus all the costs involved might be better spent possibly saving up for extended adoption leave if necessary. Consider the services available, and the school provision. There is comfort to us in knowing our kids would have 5 or 6 primaries and 2 or 3 secondaries to rattle through before we even had to consider going out of borough, all within a reasonable travel times. In a more rural area options may be more limited.
Plenty of kids live in flats, and in London especially it's not uncommon. It's about how you work things out and the lifestyle you are willing to lead. If you had a kid for whom being outside is very regulating, constantly having to go outside and sit in a park is very time intensive, and not very private if they have meltdowns. Or you go on walks, trips out, stuff like that. You need to be prepared to do lots of outdoorsy stuff potentially, and if you are a home bod, or find sitting in parks endlessly for hours tedious, a garden or outdoor space can be really helpful. However, if you travel a lot, plan on going on holidays or visiting family a lot once L.O has been settled, thats a lifestyle where a flat might work out better. Potentially more security, better location, closer to resources, airports, train stations etc.
Our cat litter lives in the bathroom, is that a possibility? Or something creative with a built in furniture piece or a modified under sink cupboard in the bathroom? I feel like Pinterest might have some ideas.