Someone has Paid for that land and owns it, It isn't government property
However, The doors are open and public are invited in therefore it is a Public
Area on Private land therefore, You have the right to shoot
on it but the Owner /person in charge / referees of the person in charge / personelle (managers / landlord/ Staff / Security) have the right to remove you from the premises, If you fail to comply they can file a tresspass claim against you (unless you live in scotland

then they need to claim ACTUAL damages if you have caused any (physical damage not just "oops I stopped shops getting customers" damage) or a Harrasment claim (which nothing happens unless you are a repeat offender, 3 times I think.