So under what legal power could the Police move folk from that area that is part of the public highway?
To start with the constable could start with simply ask them to move off the centreline using powers of persuasion (a cop can ask you to do pretty much anything they like without needing a legal power as you can choose to comply or refuse)
But if you're looking for offences or legislative powers then you can start with Actions endangering safety of aircraft (under ANO) for one (approach surface infringement which is a safety specification). Constables have power to use reasonable force to prevent the offence (i.e. move the people on)
For anyone between the hedgeline and the field boundary then they're on the highway (as the legal highway includes footpaths and verges) and must obey the directions of a constable to proceed in a particular direction.