There are a large number of ways to walk from the White Bridge to the top wood, round it, and back.
Routes up the way include going up the tarmac path to the stables and then round thro the stables wood, or up the meadow, or somewhat longer by following the river south; the path then comes out below the crematorium, so cut across to the top wood.
Round the top wood, or take the [muddy] short cut across it. Then take the zigzag back, or for a muddy diversion go up to the top of the golf course and take the steep muddy path down to the corner of the pine wood.
Then wander down the main drag past the waterfall back to the White Bridge.
To see the routes - click here.