Perhaps we have our wires crossed.

On our site, the police could only "move you on" if you were doing something illegal...causing a breach of the peace by fighting, perhaps, or intimidating other lawful users of the land.

Over here, there is no legal requirement to belong to the BMFA (our version of the AMA), to hold insurance, or to use a frequency peg of any type. So, in the case of my field, the police would have no interest in any dispute between modellers. Neither would the Local Authority (analogous to your County, I suppose).

Our field is designated as a flying site by Parliament, via the Secretary of State. It's beyond the power of our Local Authority to change that designation; so it can't prohibit model flying on that land...unless it first seeks authority from Parliament. Which is nice.