We have NT membership. We've two big very child friendly (big playareas) within 25 miles so alternate our visits to these. On holidays we try to use the membership on one of our days (or more if we can).
I follow local days out sites on social media for information about cheap or free days out or activities.
Plan ahead and book ahead to make use of offers and time to save/budget.
I have CSSC membership for free EH membership and whilst we have no real local venues we try to use when we go away for weekends or holidays. I also use this for discounted tickets to venues and have a work discount scheme for cinema. We then go to wilko or similar for pick n mix rather than buy cinema food.
I can't bear the thought of buying The Sun or Daily Mail just to get a discount - but that's just me.
Free museums.
Take picnic/snacks/drinks. We sometimes buy a £3 supermarket meal deal on the way to a day out if we've not had time to get picnic stuff/stayed overnight beforehand.
2for1 train days out, Tesco vouchers, cereal vouchers, Groupon, Wowcher
Parks - we often visit parks in villages out of our local area as such - the different setting and equipment can be exciting.
The beach - we choose a more remote beach village rather than the big town beach with arcades etc. If you cant see them you can't be pestered for stuff that costs money.
Some places do repeat visits for the price of entry - magna in Sheffield do this - check websites before you go incase you need photos etc on the day
I have low expectations for hotels - we use Travelodge mainly. It's just a bed and a shower and as long as it's clean I don't care if it's not fancy or instagrammable. We don't usually have breakfast in hotel either - will take cartons of juice and croissants to tide us over until we can get a proper good cooked one (usually something like wetherspoons - this can fill us up all day sometimes).
We also got an electric coolbox a few years ago - can use car adapter to charge it electric socket in Hotel room - it's meant we can pack some fresh items and keep them cool.
Again like previous posters people probably wonder how we afford it. But it's a real combo of the above plus like others we are extremely lucky to have an incredibly small mortgage - haven't overstretched and only run 1 smaller 2014 age car which is economical. We therefore have a larger disposable income - but i still refuse to overspend. I also think the charges for some places are extortional and out of reach for many even with discounts.