Can the local authority prevent a match taking place if the police decline to attend or if the ground management refuses to invite them in?

No.  The safety certificate lays down the safe capacity of the ground, having regard to its structure and safety management.  Public order and the prevention of offences cannot be taken into account in determining the safe capacity.  In order to reduce the capacity, the local authority would need to demonstrate that the absence of the police would present a safety hazard that could not be overcome by measures taken by the ground management.