The Saint Swithun Way was opened in celebration of the Golden Jubilee of Queen Elizabeth II in 2002 and goes from Winchester to Farnham (and is roughly where the Pilgrims’ Way once ran – the original route is now under the A31). The waymarking of this route is circles which are green and show a scallop shell with two crossing crosiers (to represent Saint Swithun and Saint Thomas a Becket). The Tourist information offices in Winchester sells guides to the Saint Swithun's Way for £3 which includes maps but these are more sketch maps than trail maps - between these and the way markers it is usually possible to find where you should be walking (we did have to guess on at least one occasion but managed to guess correctly). I wouldn't rely solely on the way markers or the maps on this section of the Pilgrims' Way.
A blog about the Pilgrimage to Santiago de Compostela