Ok, I've updated the map from what I can see on aerial imagery - private driveways to the west (with gates) and track to the east, hopefully that reflects on the ground reality. (might need to Ctrl + F5 refresh to see it).

In terms of access rights, I'd say the only other section which is excluded is in the farmyard - see section 6(1)(b)(ii) - though people could walk along the edge of the field to bypass it as allowed in section 7(10)(b): https://www.legislation.gov.uk/asp/2003/2/part/1/chapter/2 

The track in the farmyard can be made access=private? https://www.openstreetmap.org/way/749675410#map=17/56.659635/-2.576916&layers=N 