In 1856 this building was purchased by the Vestry Council of St Margaret and St John in Westminster to provide premises for a public library as described in the 1855 Public Libraries Act, thus beating other parishes by 30 years.
At its source the image is captioned "The first public library in London, at Great Smith Street (1857)".
The library function of this building was replaced in 1893 by the red brick "Old Westminster Library" on the opposite side of the street and that must be when (c.1894) it was demolished since Church House, which occupies the site now, was, partially, built in 1891 - 1902.