5705freedaysout may be able to help, but they are a bespoke service that concentrate on free attractions, history and education in the main.
They rely on donations so it may be nice to donate a few pounds, but with over 500 free days out on their books within England alone, it may be a small price to pay when you consisder a day out in England for a family of 4 may go upwards of £200.00 a day.
Just mail them
5705freedaysout@gmail.com
Leave a bit of detail on the quantity of people in the party, prefered postcode for the trip, and any other detail regarding what sort of attraction you want and the rough date of travelling.
Like I said, it is a bespoke service, but try to find anything on the internet nowadays that does not involve you spending an hour of your time, sifting through rubbish sites, only to realise, that you just wasted.