Turning left via Gabriel Street onto Chapel Street. Turning right on Chapel Street, the Methodist New Connexion Church was on the left.
The society was established 1797. The New Connexion Methodists were a breakaway group from Wesleyans in 1831 and they became the Teetotal Wesleyan Methodist Denomination. and were strictly teetotal. The Teetotal chapel existed from 1842 but it’s possible there may have been an earlier chapel on Fore Street. They later became the New Connexion Methodists and this chapel is marked as such on 1877 OS maps. The chapel closed in 1899 and became the Drill Hall when congregation relocated to the new church in Bedford Road. The Drill Hall is now a shopping arcade.
You can access some of the local Methodist records here: https://west-penwith.org.uk/wpenchp2.htm