The British Pilgrimage Trust has been tracing old medieval pilgrimage routes and have recently discovered a route from Southampton to Canterbury. It is likely that the A27 runs close to the old footpath.
It is probable that Titchfield lay on this route and indeed it would make sense. Titchfield Abbey would have served as a refreshment point at least for travellers from Southampton and it would have been able to offer overnight accommodation if needed. Titchfield is about half a day’s walk from Southampton and it is probable that the pilgrims would have trekked on to Southwick for their overnight stay.
For more information about the British Pilgrimage Trust go to this link. https://britishpilgrimage.org/old-way/