Immediately to the west is the Imperial War Museum and the Imperial War Museum Annex is to the south in Austral Street.

The terraced houses in the square surround a communal garden that is open to the public during the day. The garden is maintained by Southwark Borough Council.

In the mid-18th century, Henry Bartelote and the West family owned several plots of land in St George’s Fields, with the largest one being located south of St George’s Road, between Moulton’s Close (now the Imperial War Museum) and the estate owned by Hayle.

Colonel Temple West passed away in 1784 and his freehold estate was inherited by his wife Jane until her death, after which it was passed down to his eldest son, Temple. They were given the authority to grant leases of up to 99 years and in 1791 they granted building leases to Thomas Kendall and James Hedger for the side of West Square.

The construction of most of the houses on the north, east and west sides of the square was completed by 1794, and they remain standing to this day. The houses on the south side (Nos. 25-28), built a few years later, are one storey higher and have rectangular patterned door fanlights.

During the 1800s, West Square housed some staff of the Bethlehem Royal Hospital (now the Imperial War Museum), and the Steward’s Quarters were located in the north-east corner of the hospital grounds. King Edward’s Schools and a drying post area occupied the eastern side, which is now dedicated to sports facilities.

J. A. R. Newlands, the chemist who discovered the Periodic Law for the chemical elements, was born and raised in No. 19. A blue plaque installed by the Royal Society of Chemistry commemorates him on the front of the house.

Charlotte Sharman, a Christian Congregational church philanthropist, founded a girls’ orphanage on West Square in 1867, which eventually expanded to include a nursery, an infirmary, and a large house known as The Mansion. The Orphans’ Nest in Southwark was used as a girls’ orphanage until 1929/30, and the orphanage building on Austral Street was purchased and became All Saints’ Hospital and then, in the late 1980s, the All Saints Annexe for the Imperial War Museums. In 1884–5, the Charlotte Sharman School was built on the north-west side, requiring the demolition of thirty houses.

Charlie Chaplin lived at 39 West Square as a child for a short time.