Annual passes. NT, EH, local zoo kinda thing. Free museums.
Spend on appropriate clothing. These are outgrown quickly so they are always available on Ebay vinted and fb. Waterproofs, wellies, fleeces, walking boots and so on. Good quality outdoor wear sells on well. Buy neutral colours to hand down and sell on.
Keep towels, change of clothes, spare socks in car. You can use the towels to shield changing children.
Packed lunch. Keep picnic blanket in car.
Have a blanket rule to avoid gift shops. Remind children that the day out is the treat, not buying tat from gift shop.
Take packed lunch. This is the killer. I found I was always the one making the packed lunch. Paying for food is the biggest thing that ramps up the cost. Have water bottles washed and filled and ready to go. Take a flask with hot drinks and a pre-sliced cake. I am really cheap and would take a multipack of aldis own cornettos in a cool box. I would bring something like maltesers to bribe them to walk. One for every 200m vertical ascent.
Make sure you always have a ball or Frisbee for use on a beach or somewhere suitable. Don't use at NT or someone will start a thread about you.
All this sounds quite miserable and penny pinching. My dc are past this age now but they have lots of good memories of that time. Most of our days out were not paid for at all. The annual passes are nice to have but a map of your local area will give you loads of walks and nice places to go. The walks are the things my dc enjoyed most.
I know I have put car and many people won't have cars.
Even a paid attraction can be cheap if you are organised. At a busy attraction having a packed lunch is often a much more attractive option than waiting to be seated and having an indifferent meal.
Having a nice meal when you get home can go a long way to making up for the privations of doing all the above.
Find a local bike recycling project for properly built bikes. There are loads of these now and they are very good value. I don't really like it when people recommend spending money to save money but bikes are a game changer.
Always have a plan b. Read a book about games to play on a walk.
If you get organised as soon as you are in the door on a Friday night you can be away having a nice day out on the Saturday.
Remember that your children will remember the time you spent with them. If you are not worrying about the cost of things you will be more present with your children on these days out.
We could never have done legoland or that sort of thing. Many people would not enjoy the days out I describe but it was really that or no days out.