Several buildings were associated with the market, and were provided at the expense of the Lord of the Manor (who also did well out of the trade). There are references in Treleaven's diary to the Apple Market, the Cornmarket, and the Shambles. These had become dilapidated, and a new Market House and Shambles were built in 1827. The original cornmarket was in or near Greenhill - a deed of 1764 for the present Greenhill House speaks of the cornmarket being "opposite".
A map of the town centre in 1835 shows market buildings occupying much of the road between the present War Memorial and the Bell on one side and buildings in the Square on the other side. (This is part of the map was prepared in connection with the trial of the supposed murderers of Jonathan May, mentioned above).
The Market House blocked the end of Back Lane but as it was completely open on the ground floor, supported on pillars, you could walk through from Back Lane into the Square (see the View from Back Lane under the Market building. The new Market House of 1827 may have been similar to, or even the same as, the building known as the Butter Market by the end of the that century, which formed a shelter under which traders could spread out their goods. There was a small room over it, which was used by a religious sect for meetings. The building was taken down in the 1920s to allow the street to be widened and to make way for the War Memorial.
The Shambles at the end of its days was a long shed-like building occupying the top of Ford Street, and provided accommodation for butchers in particular. It was conveniently situated by the premises of the tanners and tallow-chandlers, who lived at the top of Ford Street and dealt with the hides and surplus fat of the animals. At one time the fire-bell for the town was on top of the Shambles (eventually, it was removed to Doccombe Chapel). There was also a mounting block which was liable to be used as a soap-box for orators.