Quarrel Wood, or Oakwoods we used to call it…
Not sure of precise ownership of some of it, there’s a residents association that can get a bit NIMBY.
If the FC are unhelpful (or the school are) there may be other bits of woodland you could access, but you’d need to find ownership and arrange permission..
There’s various bits to the Oakwoods, but ideal bit would be behind Mcintosh Drive estate really.
Lass at FC, Rachel, used to do similar woodland activities for John Muir Trust and so on so may be able to assist / guide you.
seconded on the woodland between Academy and LC — nothing there likely to be of real use, risk assessment would have a fit 🙂