You've got to wonder at the selfishness of someone turning right off the a303 into it. Must take ages due to the traffic coming the other way. Maybe a bollard or two blocking access from that direction would be a better solution that just closing it.

closing it as a byway is one thing if they want to stop accidents from people turning right to drive along it (and personally i wouldn't miss people wanting to show off their 4wds along it). But you'd have to watch they're not going to be crafty and take away its right-of-wayness as a footpath and bridleway at the same time, don't you think?