This won't help for a 4yo, but for anyone else following this thread with a younger child, The Kindergarten nurseries include elements of Forest School in their curriculum (children take part once a week). Crescent III in particular as it has a small woodland area attached to its garden.
See link below for more info. I have no affiliation to this nursery group other than my daughter being registered for entry next year.
http://www.thekindergartens.com/index.p ... est-school