Hiya. Both standard and cyclemap are incorrect here as there are two separate paths here from manor farm neither of which are cycleway.
The path leading through the field from manor farm all the way left to the end is footpath only from the north side of the gate.
Everything to the right leading to the end of the field gate directly from manor farm and through that meets with the road is bridleway. (OS 1:25)
From the gate on the far right of the field the path heading north is unoffical but not for cycling/equestrian use as it leads into the Chantry woods where cycling is prohibited and leads through a farmers field (signage)

Cheers :)