Under the Barnstaple Markets Act, 1852, and after an investment of over £15,000, the Corn, Grain and Seeds and the Butchers Market opened in March of 1855, linking the High Street and Boutport Street in Barnstaple. The Market was crowded on Fridays and several cases of pocket-picking soon occurred. To guard against this, in November, the Market Committee recommended the appointment of a Market Constable to enforce the byelaws and maintain order in the Market every evening from six o'clock to eleven o'clock and on Saturdays to twelve. Additional duties included keeping the Market swept, removing the forms after the Market and, after business on Saturday nights, washing down the pavement in front of the butcher's stalls, although the latter was later provided for in the byelaws for the butchers to do themselves.

Mr William Williams, or 'Jesse', as he was more familiarly known, who resided adjoining the Market, was appointed Market Constable with a salary of £20 per annum. The appointment was made by the Town Council, under the Act, as opposed to the Watch Committee, who were responsible for the appointing of the Barnstaple Borough Police, such that he did not report to either the Barnstaple Borough Police or the Watch Committee of the Borough. However, in February of 1856, the decision was made to bring the Market Constable under the supervision of the Superintendent of the Barnstaple Borough Police. The Borough Police also developed their own presence in the Market. On Market Day, in addition to the Market Constable, as there were more robberies committed there than in any part of the Town, there were also two Barnstaple Borough Policemen stationed in the Market, one of them in plain clothes.

As the strength of the Barnstaple Borough Police had recently been increased from three to five men in 1853, there was some opposition at the outset to the additional employment of a Market Constable given the expectation the increase to the Borough Force was in part in anticipation of the extra duty soon to be required at the Market. However, no changes were made to the arrangements, with the strength of the Borough Police continuing at five until March of 1857 when PC Ridd resigned to leave for America. For reasons of economy, the vacancy in the Borough Force was not filled until the need was forced by an uprising by a large body of woolcombers that took place in the High Street, passing in front of the Borough Police Station in broad daylight without intervention. With the now smaller Force of Constables of the Borough on duty at night, the Superintendent could not maintain an Officer at the Police Station during the day. Anyone seeking assistance was greeted with a locked door during the day.

Although the Watch Committee responded by appointing a Constable to return the strength of the Borough Police to five men, when it was put to the Town Council they were opposed to paying both the salary of the Market Constable and now a "new" Policeman. The Council's refusal to approve a salary then made moot the appointment of the new Constable. Instead of a new Borough Constable, members of the Council proposed several alternatives including making the Market Constable a Constable of the Barnstaple Borough Police Force but it was argued by some that, as the Market Constable, Mr Williams performed his Police duties partially and inefficiently; by 1857, he was required by his scale of duties to be in the Market from eight in the morning until night, but he was noted as seldom being found there. Further to this the offender in a case of nuisance in the Market being held at the time had been detected not by the Market Constable but by the Borough Police. Attention was also drawn to the fact Market Constable Williams did not meet the height regulation that had been adopted for the Police, although Sergeant Chanter of the Borough Police was also lacking in stature, but he was appointed before the requirement was put in place.

Yet another proposal was to continue the Market Constable appointment, with Market Constable Williams in the post, with the said Constable giving such assistance as general Policeman as the duties of his Office allowed in lieu of the Watch Committee appointing a replacement Constable for the Borough Force. The duties of the Market Constable with respect to cleansing the Market would be transferred to the renter of the tolls of the Market. In this way 16s or 17s a week could be saved, the salary of a regular Policeman, but the Council had no power to appoint a Constable that could act outside of the Market and it meant the Market Constable would be under the control of neither the Watch Committee nor the Superintendent of Police.

The strong feelings amongst many in the Town Council against either continuing the post of Market Constable or to bringing the Borough Police Force up to their previous strength eventually led Market Constable Williams to submit his letter of resignation to the Mayor and Town Council in August of 1857 with the position of Barnstaple Market Constable ceasing thereafter: