Without any old track diagram references I couldn't say if there were any additional parallel tracks along here.
According to pathetic motorways the route of the road mentioned was planned to be part of the abandoned M272 Portswood Link
http://pathetic.org.uk/unbuilt/m272/
I would expect the width required would have been safeguarded for that purpose and opportunities taken to acquire parcels of land progressively along the route over many years.