Apparently named after the district of Newington in the Borough of Southwark, South London. Nearby, Camberwell Terrace (originally Camberwell Street) and Camberwell Court are also named after a suburb of South London. However, the theme does not appear to go any further.
As well as this street and Newington Street, the name Newington has been adopted for the wider district adjacent to Antrim Road and Limestone Road, e.g. in the name of Newington Amateur Boxing Club.