The "modern" NATS - nor any of its predecessors ever provided services in the Channel Islands.
I can recall a conversation with a long since retired ATCO, who said he had worked at Guernsey Airport, back in the days of 'The Ministry of Civil Aviation'. Perhaps he was on 'secondment', or did the MCA have the contract, way back then?
I was under the impression that for at least the past 30 odd years, the States of Jersey and Guernsey have directly employed their own ATCOs.