I don't think any of your outgoings are 'outrageous' but some of them could be cut back or even eliminated as others have said.
So...do you really need to have your nails done each month? If you have the money it's a nice to have, but if you want more money in your pocket just do what we used to do and manicure at home. It was never a 'thing' to have your nails done when I was in my 20s (almost 40 years ago), it used to be a pleasure to do a home manicure and varnish, then maybe have a tidy up manicure at a beauty salon every six months or so to keep the shape.
Are you both running smaller cars? If not, because you need one 'family sized car' could one of you downgrade that to save on petrol (I know £100 is unfortunately the average now but if they're both gas guzzler cars is that a potential saving?)
Stop the takeaways or make them a once a fortnight or once a month treat - taking it down to a fortnightly one gives you £75 back automatically. You don't have to give them up completely, life has to be about a few pleasures even if it's just a walk on a beach! And if you can afford a takeaway but want to save, just cut back.
Can your 'date nights' be changed? I don't know what you do but could, for example, the kids go to grandparents for the night and you two just cosy up with Netflix? Or could you make it a 'date day' and drop the kids off then go for a walk in the country or beach. We sometimes just head to a town or village we've not visited and have a mooch around antique shops or markets!
As others have said you can get National Trust and English Heritage (or the equivalent) combined for the £20 you're spending on the zoo and that opens up loads of places and further afield.
A lot of places also do the 'upgrade your tickets to annual passes' for nothing nowadays so if you're having a day out somewhere always ask. For example, Blenheim Palace does a family of four ticket for £84 or thereabouts. But you can upgrade, for free, to an annual pass which means you can visit as often as you want. That's £6.95p for the four of you each month if you want to cost it out. Leeds Castle in Kent does the same for a family of four at £99 for the original ticket. It's a way of adding trips out throughout the year for 'nothing' if you're going to a place anyway and shelling out for that first trip. It's always worth asking if they do an upgrade to an annual pass.
Do you use Nectar or Tesco points? We did days out for a whole holiday in UK using Tesco points a couple of years ago! Didn't 'pay' for entry to anywhere. And managed to get a meal out of it too. Just by saving the points from our weekly shop. You can use Tesco points to buy English Heritage membership for the year for example. That basically means you're getting it for 'nothing' as you'd be buying the food anyway. And Blenheim Palace tickets can also be bought with Tesco points - then you can upgrade for free to the annual one before you leave the place!
And, finally, down grade meetings with friends. We now meet up in the local park with a takeaway coffee. Or we head to the beach or park, bring a bottle or two of wine between us, someone gets nibbles, someone will bring some cup cakes or something and we'll have a girls day picnic instead of a girls night out.
Socialising doesn't have to be in a restaurant or pub, nor does it have to be at night. Just going for a walk in the country with mates can be lovely - take a packed lunch each and just enjoy the friendships.