Hi Cathy
They always manage to chuck in a curve-ball somewhere, don't they (our ancestors)

I did notice that on the 1851, George ADAMS age was 41 (b abt 1811, not 1815) and a baker/Grocer 7 employer, and in 1841 he is age 31 (could be rounded though) with occupation Clerk, - could not see any to fit him b 1811 or 1815 on the later census - but since it seems to be the right family, owing to son George W....
1871: 6 Fir Grove Terrace, Millbrook, Southampton, HampshireRG10 / Piece: 1200 / Folio: 85 / Pg 4
Head: William SEARLE 67, Grocer, b St Georges Han'er Sq., London
Wife: Elizabeth SEARLE 60, b Nursling, Hants
Dau: Sarah SEARLE 28, b Richmond Surrey
(Reg District covering Millbrook is : South Stomeham)
1881: Firgrove Road, Millbrook, Southampton, HampshireRG11 / Piece: 1223 / Folio: 16 / Pg 26
Head: Will'm SEARLE 77, Tea Dealer, b London
Wife: Elizabeth SEARLE 70, b Nursling, Hants
(I think the ecclesatic parish for the above is Fremantle, Millbrook)
Will have a look for George W in 1861

I did see these:
DEATH: of a George Henry ADAMS, Alverstoke , Sep Qtr 1856
(Can't see any George ADAMS death in South Stoneham or Southampton districts 1851-1861)
MARRIAGE: Southampton , Sep Qtr 1860
Elizabeth ADAMS and William SEARLE on same page
Cheers

AMBLY