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Londonist's post about this house and Newton's observatory is excellent. They have a picture of the house in about 1900 (from the lady's costume) and it already has a plaque, but not the one we've photographed, as far as one can tell. There we also learn that Fanny Burney and her father lived in the house c.1770. By the 1860s the house seems to have come under the ownership of the Orange Street Chapel next door, because the observatory was sold to an American to pay for new pews there.

The post goes on to say "... in June 1925, the City Council of Westminster bought the site from the Orange Street chapel in order to make way for the Westminster Arts Library. The fabric of the building was bought as an item by a certain Hugh Phillips Esq. who took measurements and had it dismantled carefully with the intention of reconstructing it elsewhere as a 'long lasting national memorial to England’s greatest natural philosopher'", but this was never done and both the fabric and the observatory are lost.