I was too young ever to see him in action. He looks a little like Oscar Wild.    The location can easily be identified: this is about 50 yards west of the bandstand on the Promenade (you can see the connecting bridge in the background top right) and near the Hove boundary.

I do not know if it has any connection with this man, WH Shoosmith, but there's a WW1 grave of a soldier from the 2nd Bn Royal Sussex Regiment with such name in a military cemetery in France. Could be him, who knows?