Panorama heard from a postman that his route could not be done in the given time. So, we asked British Military Fitness instructor Tony Goddard to test Martin Heward's round for us, while we timed him. Could he do it in the time?
Reporter Vivian White met Tony, a former marine, to find out what the recommended walking speed looked like.
The Royal Mail said its own testing of the route in Nunthorpe on Teeside showed that it could be done within 3.5 hours and "completely reject" the suggestion it cannot be achieved. It said that Panorama's exercise "shed no light whatsoever" on the method it uses to design its routes.
Panorama: Can't Deliver, Won't Deliver, BBC One, Monday 14 December at 8.30pm.