There is life and savings at the other end. Though you do have to remind yourself from time to time where all the money you both earned went.
A good nanny who takes 3 kids through the witching hour, home work done and baths is a godsend if you are both in a high stress job with employers/customers who demand high performance and long days. See the lack of savings as an investment but that said you might need to sit down with your husband and see if there are cut backs elsewhere. Cars, holiday, personal spends/birthday and Christmas budgets. Often when in a high income bracket where you frankly work your ass off for the return it is easy to justify to yourself why you should have some rewards. But if your mutual employment is precarious and your outgoings high by necessity then other cut backs might be sensible to build some contingency in.
I personally wouldn't cut back my hours, go part time or the rest. We started out very much like you both holding down long hours, high stress and highly paid jobs. A really hamster wheel when the kids were little. Keeping my job and my career has given us more resilience through periods of unemployment for my other half and looking back now it has been worth it all for both of us. Assuming your other half also pulls his weight at home.
A friends kids are year 5 & 7 now and she has moved to an au pair "plus" model. The downside is it's live in, so you need the space in London but it's more low key, the kids are supervised for homework and pick ups and some work dinners. Overall life is lower stress financially. She swears by antipodean au pairs, they can usually all drive, tend to have a more outdoorsy outlook [she has boys] and are more willing to get stuck in and have a go when there's a problem rather than make it hers.
We never did the au pair thing. Moved from a nanny to a great childminder with kids the same age later in the school years. As her kids grew and needed to study, so did ours so it worked for us. She had some small kids in the morning for part timers. You can find the right blend as time goes on and your kids grow a bit. For now, expensive as it is it sounds like you have the right blend now.