In 1853 in London and 1854 for the provinces the government introduced an Act which forced many churchyards to close. Southampton town council was one of the earliest to open a municipal cemetery in 1846, orginally named Cemetery by the Common, later Hill Lane Cemetery and from the 1990's Southampton Old Cemetery. There is an active group Friends of Southampton Old Cemetery [has a website] which assists in locating graves within the 27 acres site [approx 117,000 burials]. Prior to its opening the main burial ground was St Mary's churchyard where on occasions the burials were so many that the height of the burial ground went 10 -14 feet up the side of the church building. It is said that stray dogs sometimes appeared with a bone in the mouth. The Church of England was very reluctant to give up the lucrative income to conduct burial services and insisted that burials in the council owned cemeteries should still be required a burial fee to the clergy at St Mary's which was in addition to the burial fee at the cemetery about a mile away from the church. The cemetery initially had C of E and Non Conformist plots but shortly after opening the Hebrew community were allowed a Mortuary Chapel and a walled section of the cemetery for Jewish burials - this was the first Jewish public cemetery in Britain. Much later the Roman Catholics were allocated plots but were not allowed a boundary wall and not allowed a Chapel for services. As the town expanded the council added more cemeteries Holybrook at the end of 19th century, St Mary's Extra, Millbrook [at the rear of Holy Trinity Church] and Stoneham. The city bereavement services has had major cuts in staff and prior to those cuts had notices up that a search of any burial records would take 5 to 8 weeks, I suspect it is now a much longer wait [fees are payable].
If you go onto Royal Mail.com postcode search and enter 3 Bedford Place Southampton SO15 2DB a map appears. Kingsland [originally outside the boundary of Hamwic the saxon area ie The King's Land still exists] but is in part of St Mary's Street and a modern trunk road dual carriageway, going onto Google estate agents show property in Kingsland Place but I suspect this is a modern day adaptation of the name but again using Google on Royal Mail.com postcode search St Mary's Street for approximate location. For details on the location of Brewhouse Lane destroyed in WWII see
http://www.plimsoll.org/resources/SCCLibraries/2062.aspThere is a St Nicholas Greek Orthodox Church, St Nicholas C of E Bassett, Southampton and St Nicolas [the church with the one hand clock] at North Stoneham. possibly Hampshire Genealogical Society may be help to help on information re burials.
