Harrumph. Well now I know why it looked like only 1 mile on the route map to the rest/mechanic point at Roydon. They've drawn the blob on Nazeing instead of on Roydon. And Nazeing was indeed about a mile from the breakdown because that's the bit we did at walking pace. Oh well.
Full route: http://www.gmap-pedometer.com/?r=316723.
The elevation widget is really cool, you can see just how steep each bit of hill was!