After meeting for a number of years in a cottage from which the internal walls had been removed, the Primitive Methodist society at Middlestone Moor laid the foundation stones for a new chapel in 1891. It was in the Spennymoor station. The March 1892 magazine reports the completion of the chapel (although it spells the village as Middleston).
Ordnance Survey maps from 1896 show a Primitive Methodist chapel on the west side of Durham Street. The building still is in place and used as a dancing school, although Street View does not let you read the datestone over the door.
Primitive Methodist magazine September 1891 page 571
Primitive Methodist magazine April 1882 page 250