Hopscotch Botley have a very large garden and spends lots of time outside, or the ymca fairthorne manor could be another to look at - personally haven’t had experience with this one for few years now but I know they have large acres of fields and forest to explore.
Little Griffins/Wild griffins at West Hill Park School. They had an open day yesterday. It’s a preschool though, so it’s for 2.5 years plus. They have indoor and outdoor provision, you can mix and match or go all indoors or all outdoors.