Like many things, there is no specific law directly applied to A-boards and the like - however, they can fall under a number of other laws. 'Obstructing the Highway' and suchlike are the usual ones.
It all depends on how your local authority chooses to interpret and apply these laws, and will take into consideration who owns the frontage, how narrow / busy the street or pavement is etc.
They will consider whether the sign causes an obstruction or constitutes a hazard either by its position or design.



