On 30 December 1348, Bishop Ralph made over to the vicars ‘the dwellings newly built and to be erected by us for the use of the vicars, and ‘quarters with appurtenances built and to be built’. The houses were built in two rows running north from the Hall, and were completed by the time of Bishop Ralph’s death in 1363. The quadrangle was finally completed with the building of the Chapel at the north end in the early fifteenth century. The Chapel was dedicated to the Assumption of the Blessed Virgin Mary and St Katherine, and it is first mentioned in a charter of 1479, but shields on the Chapel door carry the arms of Bishops Bubwith and Stafford, suggesting that the chapel was begun in the episcopate of the former and finished under the latter, giving it a date of c.1424-30. A room over the Chapel served as the Vicars’ Library.

Bishop Ralph made it quite clear in his original deed that each house in the quadrangle was designed to accommodate one vicar. The original houses numbered forty-two (22 on the east side and 20 on the west) and were more or less identical. Each had a ground floor room, measuring 20 feet by13 feet (6 x 4 metres) with large windows, one facing east and the other west, so that shutters could be closed on the windward side in the days before windows were glazed. Here the vicar read and studied. A wide, low arch led to the newel staircase, which opened into the upper room where he slept, and outside the back door into the yard there were washing facilities and a latrine, possibly under the projecting stair wing. There were wells at the top and bottom of the Close.

Despite the fine new buildings, about a century later when Bishop Bekynton held a visitation of the Close in 1459, he found much amiss. The hall and houses were dilapidated and he insisted that the Vicars must keep their houses in good repair.

The towering chimney shafts, which are such a delightful feature of the Close, were built to extend the original chimneys (possibly because the Vicars were beginning to burn coal instead of wood and taller chimneys were needed to carry away the more pungent smoke) and each carry two heraldic shields, one adorned with the arms of Bishop Bekynton, who died in 1465, or that of the bishopric alternately, the other with the arms of his executors, Hugh Sugar, a vicar, and John Pope and Richard Swann who were canons in turn. In about the mid-fifteenth century the Vicars also asked for, and were given, gardens nineteen or so feet long at the front of each house; each was walled, with an arched gateway, and it was this that changed the appearance of the Close from that of a college quadrangle to the street as it appears today.