There was a ride from Ashurst to Lyndhurst to celebrate the official opening of the new cycle route, on Friday October 6th. John Buckley of Hampshire Cycle Training attended, and you can read his report, complete with pictures. His final comment on the route is
As a route it may suit families and less experienced cyclists riding from Ashurst to Lyndhurst and back. I think the surface is too rough for roadies, and others may prefer Forest trails. It could encourage new cyclists.
However, the shared-use Lyndhurst end worries me for safety.