Hi John. I'd like to know as well! The vast majority of the stone was taken to wharves on the south bank of the Thames, where it seems to have been stockpiled, and then taken on the river, either to the city, or upstream to Middlesex, or downstream to Essex and Kent. A small amount was used locally.
It wasn't until 1805 that a transport 'infrastructure' arrived in the form of the Croydon Merstham and Godstone Iron Railway, which took stone north to Croydon, where there was an end on junction with the Surrey Iron Railway to the wharf at Wandsworth, or after 1809 onto the Croydon Canal to Deptford.
Before 1805, the only way to move the stone was by cart on the old roads and tracks. Medieval traffic would have been either by ox team or by horse and cart.