Not quite correct.  The area/path marked as “Promenade” on the map is open and accessible to the public with no restrictions.  The raised area/path in-between the Promenade and the Queens Park flats is indeed private and has a usually locked gate to protect this area.  You do not have to use the road.  To carry on along the Prom you turn right at the gate and proceed down the slope following the concrete path, this will guide you around Queens Park flats.  The path then rises up again above the beach.  