Been trying to contact the appropriate people for 2 weeks, finally got a response from:

Nigel Ilsley
District Parks Manager
Greenspace Services
Walsall Council
Tel. No. 01922 654372 or 07983970389

This was his answer:

As long as your not digging holes or causing any other form of damage we don't have a problem. However if you are digging holes etc then we'll treat it like metal detector users i.e. 200 annual licence (each) & all damage has to be rectified at their cost.

As long as we dont dig holes, permission granted...

(aka Stuart Davies)