I'm fortunate to have a a beautiful walk minutes from my house in the Dollis Valley Green Walk (pictured above and below) and so we do manage to get out into nature fairly frequently. This is a really great walk to do, especially as they have recently refurbished the playgrounds along the walk. At times you can really feel like you are in the middle of nowhere.
Other good local places to walk and explore nature that I know of are Aldenham Country Park, Adelaide Road Nature Reserve (Camden), Camley Street Natural Park (near Kings Cross), Long Lane Pasture (Finchley), and the Parkland Walk that runs from Alexandra Park to Highgate Wood as well as obviously some of the wilder parts of Hampstead Heath including the parts by Spaniards Inn and the top of the Heath extension.
I've also come across two groups recently that encourage exploration of nature, that sound really enjoyable and something different to do with children:
Nature Play North London, Highgate Wood
They set up blankets in a cosy nook in the wood. When they are settled, snacks and drinks can be shared, and then it's about freedom for the children to explore and discover their surroundings and abilities!
You can find out more by visiting the site or joining their Facebook page.
Babies In the Park, Avenue House Park
This is described as a conscious walk in the park connecting to nature and meets at the Avenue House Kiosk. For more details check out the Facebook page.
Do you know of any other groups or good places to go that are on the wilder side? Do let us and other parents know.