Heya,
I cycled Wolf Way from the War Memorial to Icklington as part of my ride, and from my observation it only seemed to be closed to Motor Vehicles (The large vehicle gate was padlocked shut, but the pedestrian/cyclist gate was perfectly usable. There were no signs either way, and I met a few walkers on my ride and didn't get any indication we weren't supposed to be there), therefore, I changed "motor_vehicle=designated" to "motor_vehicle=no". I removed the "access" tag as it was redundant, having been overridden for all vehicle types.