The 1867 register of non-conformist places of worship records the Primitive Methodists meeting in “building in the occupation of George Noble” in Frogmore, East Meon.
The Primitive Methodist magazine of September 1894 records that the memorial stones for a new place of worship had been laid at East Meon. It was in the Buriton station.
The 1869 and 1908 Ordnance Survey maps show a Primitive Methodist chapel to the south of High Street, set back behind the houses that front the street. On satellite view in 2021 it appears that the chapel still exists.
You can read more about the chapel and see some pictures on the East Meon History archive.
Primitive Methodist magazine 1894 September page 717
East Meon History Archive accessed June 28th 2021 at: https://www.eastmeonhistory.org.uk/content/catalogue_item/chapels/primitive-methodist-chapel