You need to go through you budget in finer detail. The Martin Lewis Budget planner is really good.
I can't see how you're not overspending if what you have here is right. I also think some is missing. Like how is your mobile phone/ TV / internet £39 total for 2 people? And as a PP said, no TV licence, car maintenance, MOTs, other subscriptions e.g. netflix or prime, gifts, going out, days out, parking, even the occasional takeaway or meal out? It all adds up.
To answer you question though, here's what I would consider doing:
Think about the couple of years ahead. It won't be like this forever. Childcare costs can drop once they get over 2 and will drop further once they're getting the free 30 hours.
Find a way to drop the second car if you can - whether it's getting a nursery or childminder within walking distance.
Make sure you're signed up to all government offers - Do you have a LISA?
Minimise rent. You can get flats with gardens and tbh if it's for a focused 2,3 or 5 years you can get by without one. Many of us do! It's brutal but move if you have to. It'll cost you about £1000 to move (plus the deposit, but you'll hopefully get your current one back so that should cancel out). But if you're saving 200-300 a month you'll soon make that back in 6 months
Look for a job that pays more and doesn't involve travel.
As PP have said, sell toys, baby stuff, clothes
Buy as little as possible and ideally second hand from now on to move your spending into assets
Make yourself a savings plan to stay focused and motivated otherwise it seems unachievable.
Btw I have a lot to say on it as I have done this myself to get out of £15K debt during the pandemic. It can be done but you need to set yourself goals otherwise it is demoralising!