My number one recommendation is make space for a dishwasher. The sheer amount of time, energy and space they save is totally disproportionate to their cost - get one with an anti flood device, though. Because you're in a flat. And always scrape the plates off properly the moment you take them into the kitchen and put them in there rather than on the side and get into a habit of before you close it up, make sure the spray arm can rotate freely by giving it a quick spin.
Pick a day for bedding and stick to it. Say, Tuesday morning, everything goes into the machine and you put a clean set of things on straight away, rather than trying to find the energy to do it when the originals are dry. Use the time it takes for the kettle to boil to run over the floor with a mop. I like my steam mop, as it saves buckets - the head then goes in with the towel wash (which is next on the list) and the bedding doesn't get dirty coming out of the machine if it touches the floor.
If you can, once the floor's done and the machine is running, go and put fresh bedlinen on - it's much better than leaving it until night time when you're knackered, as it doesn't matter how tired you are, the bed is all ready for you.
I would seriously consider getting a Eufy if it were just me here. If that's not realistic, vacuuming more often means it takes less time overall, as nothing gets so bad you have to keep going over and over the same bit. If you need to wash a filter, get a spare so you can do it each time you vacuum and keep them on continual rotation. Or get a machine with a self cleaning filter setting.
Having a cloth and spray (whether water or a cleaning solution) in each room is really useful, as you can quickly wipe over something as soon as you spot it's dusty or grubby, which takes seconds, rather than the best part of an hour.
Clothes go into the linen bin straight away. If they're on the floor, they get picked up straight away and put into it as soon as you spot them. Children are pretty good at searching for clothes. Especially if they are 'trusted because they're big enough' to load the machine, put the powder in and set it running. The smaller one can be in charge of putting a dishwasher tablet in, closing the door and pushing start.
I still have sort of allocated days. Clothes washing is done on Friday night, bedding on Saturday mornings, but the kitchen is generally kept clean and bathrooms are done daily after a visit so they never need scrubbing from top to bottom.
Other than that, chuck toys into a tub and they go to bed with the children. You don't need to be looking at them all evening.
I grew up in a shithole. I'm never having that in my own home - but it's really not that bad (one reason why I can't stand how awful my childhood place was) if you keep doing little things often.