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I think that the current 3 and 2 Church Street (built c.1972?) were on the site of the previously numbered 1 Church Street.
From the Inclosure Map, April 1814
Common Rights:
1 Church Street used to attract Rights of Common, but these are now associated with the Tri-Service Station. However, I am unabel to see John Lambourn on this record:
Sanden Fee Commoners' List, 1847
John Lambourn’s House, 1 Church Street, c.1848:
The article on the Church of the Latter-Day Saints in Hungerford includes the following reference: The source for this as a meeting place for the Saints in Hungerford comes from a sheaf of handwritten papers known as the Jensen Collection and is held in the LDS Church History Library. There are seven small sheets of paper of notes in pencil that relate to the church in Hungerford and on page 6 it records ‘Bro. Jn. Lambourn residing at 1 Church Street, Hungerford, was President and the Saints held Divine services at his home.’ John Lambourn and his wife Martha were baptised on 4th April 1850 by Thomas Squires and the 1851 census shows that they lived on Church Street where John was a shoemaker.
I think this was the house standing in front of the "Meeting House" shown in the 1814 map above, now the site of 3 and 2 Church Street.