I totally get the feeling of having worked hard and put up with a lot to earn a lot. But you are making some luxurious choices here, ones that that be honest your income just doesn't stretch to. You both earn well, but not megabucks - not multiple hundreds of thousands a year each like many in London do, especially those with full time nannies.
I have pretty successful friends, everyone earns over £100k and some much more (including bonuses). None of them have a full time nanny. (some do nanny shares). None of them pay for a nanny PLUS nursery - take it from me as someone with a specialism in this area, play and socialisation is the best education for under 5s, and your nanny can very easily provide this for your youngest especially by taking them to meet ups and play groups with other nannies, which are very common. The fact your youngest was "jealous" when their older sibling started school is a ridiculous thing to give into.
I also don't know anyone - and to underscore I know couples, both working, with 3 kids, who take home around £3-400k a a year between them - who have a cleaner for 5 hours a week. And they live in much bigger properties than you!
Honestly, you seem to think you can afford a lifestyle that simply isn't reasonable on your income. And then when you feel you've no money left, you wonder why you're feeling strapped.
Cut the nursery out or massively down.
Cut the cleaner back to 3 hours a week.
Figure out a way to not need a nanny once all the kids are in school. There are alternatives and they are alternatives that the vast majority of working parents cope with!
Ask yourself what is more important - ironing, or being able to save for big future goals? Surely the latter??
And you'll have hundreds more a month just from that.
Online shopping from a cheaper grocery store could also reduce your food bill while still being convenient (I get how tiring meal planning and shopping is when you're working and have kids.)