Have been wanting to attempt this route for a while. Lovely run through the forest and easy to jump on the tube to get home!
Looking at the gpx I found for the route there does seem to be a few drifts and straight lines. I tried to map a route that followed the most natural route through the forest using the trails and bridleways in order to reach the way points. There were some small points I have noted:
Crossing Wansted Flats - There are bits here where there is no path as you are crossing an open grassy field. As a guide look for the group of trees ahead and aim for the left hand side of this group. As the grass returns to being rough and long again, keep this to your left hand side until you reach the trees.
Crossing Woodford New Road - The gpx i found has the route going around the pond on its right hand side. However I run past this a lot and although there is a path on the map, I have never seen one there. I have added a photo of that part. Not sure if the pond has gotten bigger over time but crossing the road and going around the pond on its left side is a bridleway which seems much more natural and there are clear trails to and from the road.