The first step is to check a last-known address in electoral registers or telephone directories. We hold extensive collections of Hampshire electoral registers up to 2002. We also hold some telephone directories: for Portsmouth and Southampton, 1944; Bournemouth, 1948; and a selection of areas and years, 1969-2006. Local libraries may also hold old telephone directories for their area.
Online, you can search electoral registers, 2002 to 2008 at www.192.com and telephone directories, 1880-1984 at www.ancestry.co.uk. Both are subscription websites, though telephone directories can be searched through Ancestry for free at Hampshire Record Office and some Hampshire libraries.
If you are looking for long lost relatives, The Salvation Army runs a family tracing service.