I suggest you start by finding out which the departments at your local council is responsible for this 'park'. Although you describe it as a 'nature reserve', such open spaces are not typically aligned to areas that allocated for playing in (Recreation / Parks), so I suspect this is merely an open space, not a space allocated to promoite wildlife.
You entitled your post 'Planning Permission'. Whether planning consent is required really depends on the allocation of the space. If you talk to Development Control at the council (the PP people), they should be able to confirm what allocation this particular space has. If it is already a recreational space, PP is probably not required - nevertheless the department responsible for it must have had some internal discussion/decision-making process to decide to approve funding/expenditure for it - so you could try questioning what consultation process they went through.
I wonder what your concern about having such a use is?