As you say, Discovery, downstairs at Northampton Central Library is the place to go, and they can help you with these questions. My knowledge comes from carrying out detailed street history research on the area and I have been a Heritage Open Day guide to the Guildhall including the basements. There is plenty of material available to resolve the original question, but probably the simplest is to read the sections on the town gaol in Cox "The Borough Records of Northampton" Vol II 1898. I did try to elucidate because you need to differentiate between county council premises (south of George Row and in Angel Street/Guildhall Road) and borough council premises. You also need to be aware that building locations change over time. Hence before 1860 the Guildhall was located on the south side of Abington Street at the corner with Woodhill (most of this went with street widening in the early 1900s). The cells on Fish Street precede the cells under the Guildhall. St Giles Square denotes the first part of St Giles Street, but was not physically a square as such, just classier houses either side. A lot of the problems you seem to be having arise from confusion between county and borough premises, and assuming the guildhall was always where it is now.
