Below the medieval building of the Saracen’s Head there was reportedly a vaulted cellar, which extended eastwards as far as the corner of North Street.
Vaulted medieval cellar in Bayley Lane, Coventry
CC BY-SA 2.0

It has been suggested that the original cellar lay below a single large building, either for a religious order or as part of the mansion occupied by the Marmion family.
Harry Lupton (who wrote A History of Thame and its Hamlets, 1860) suggested that the arches were removed by the brewers before 1860 to make room for casks. Building work was also carried out after World War Two, and no medieval structures can be seen today.