The Hampshire Genealogical Society have a county wide comprehensive burial index up to the beginning of civil registration in 1837.
Simon's age at burial would put his birth at circa 1745. Bearing in mind the rounding down of ages to the nearest 5 on the 1841 census Ann's birth year would be circa 1766. This would put her age at 39 in 1805 and Simon's at 60 - therefore a possible second marriage for Simon if Ann was indeed his wife.
As yet the Hampshire Genealogical Society have only a baptism index starting in 1813, but they do have a countywide marriage index up to 1837 (Hampshire is not well served by the IGI - best estimate is about 43% coverage of parishes pre 1813 so more not covered than covered)
http://www.hgs-online.org.uk/But I believe their indexes may be searched only for members of the society.
1871 census RG10 1194 folio 50
4 Anspach? Place St Michael Southampton Hampshire
John Rose 66 Southampton, Hampshire, Head Married Carpet beater
Hannah Rose 40 Beaulieu, Hampshire, Wife Married
Mary E Rose 15 Southampton, Hampshire, Daughter
Hannah E Rose 9 Southampton, Hampshire, Daughter
Joseph Rose 7 Southampton, Hampshire, Son
William Rawlance 20 Beaulieu, Hampshire, Stepson Porter
1861 census RG9 679 folio
Southampton St John Hampshire
James Rose 22 Southampton Head Married Sailor
Amelia Rose 35 Southampton Wife Married
Ann Semes 74 Isle of Wight? Widow
next door
Vile Lane ? Court
John Rose 56 Southampton Head Married Licensed Porter
Hannah Rose 30 Beaulieu, Hampshire, Wife Married
Marey E Rose 5 Southampton Daughter
William Rawlance 10 Beaulieu, Hampshire, Stepson
John only appears to have his daughter Hannah with him on the 1881 census.
Regards
Valda