I can't believe four of you live in that tiny flat. Where are all your clothes, shoes and coats etc? I have to say for four people living like that you're doing a fantastic job, you've practically no stuff v what an average family of four would have.
Unfortunately your storage solutions are cost effective and practical there are not aesthetically pleasing.
I don't think uou need to move out, but you need to put more stuff away. Get a proper bed with a head board and with storage drawers under it, you can get guard rails for kids if yours falls out that just clip onto the side.
There is also nicer ways to store your belongings as others have pointed out, you don't need to use plastic tubs unless theee is a financial issue.
Take the desk table and chair out, declutter, get some decent storage items, take a trip to IKEA, and maybe spruce up your balcony a bit, it's tiny and would only take a couple of hours, you can get stuff from b&q to get rid of the algae then stain it. Some nice plain white bed linen and some nice throws on the beds in the living room.
It's a couple of days work, for a few hundred quid max, that will save you ten grand at least.