This might be one to take to appeal.
IMO, you do need better evidence that the wood exists. It isn’t named on Google Maps, but is on OpenStreetMap as the “Black Country Millennium Forest” - Way: Black Country Millennium Forest (267426829) | OpenStreetMap
I would advise you to find some other references too (council etc) and place them in the supporting text or appeal text if you are taking it straight to appeal.