This photo came from West Greenwich library and is described as the Borough Hall. You can make this out on the awning on the front on the building. The Borough Hall was originally on the site that is now Meridian House. You can see it labelled on the 1914 map
here, so must date the picture to pre 1937 (the date Meridian House was built). I think the building on the right is the back of
Greenwich Bath House (once on the corner of
Greenwich High Road and Royal Hill) and the building on the left is the public house that once stood on the corner of Peyton Place and Royal Hill.