I’m not sure about the derivation of ‘Windlesham Road’. Windlesham is a large village in Surrey and I can’t see any obvious relevance to the Salisbury area.
A couple of the streets in the immediate area are named after wards at Salisbury District Hospital (Beatrice, Breamore, Radnor) or large houses (Balmoral, Breamore again, Broadlands). I guess it’s possible that Windlesham was a ward either at Odstock which has since closed down or one of the wards at the Infirmary.