There are two Falkland War Memorials to be found in Southampton (that I know about), although you really need to know where to look. The first may be found inside The Holy Rood Church in Southampton.
The second may be found at Mayflower Park, between the basketball court and the fence by the close to City Terminal. The memorial was erected by the Southampton Junior Chamber, simualtaneously with the Junior Chambers of Coventry, Liverpool, Plymouth, Portsmouth and Sheffield on 11 November 1982. A Falklands Memorial may also be found within the grounds of the Tower Hill Memorial in London