The only George Brown, Sergeant in the Grenadier Guards in the 1871 British Army "Worldwide Index" has the number 1536. I can't find any other army record for him.
However this 1871 census entry seems likely:
St James' Park, Buckingham Palace guardroom:
George Brown, unm, 26, Sergeant 3rd Battalion Grenadier Guards, born Notts, Kirkby in Ashfield
(Piece 357 folio 3 page 1)
There is this George Brown on 1851 census living
Church Street, Kirkby in Ashfield, Basford, Nottinghamshire
Samuel Brown Head F W K b Kirkby, Nottinghamshire
Ann Brown F W K bMansfield, Nottinghamshire
Samuel Brown b Mansfield, Nottinghamshire
George Brown b Mansfield, Nottinghamshire
John Brown b Mansfield, Nottinghamshire
Elizabeth W Brown b Mansfield, Nottinghamshire
HO107 Piece 2125 Folio 51 Page 27
Possible marriage FreeBMD
1841 Mansfield
Samuel Brown
female name same page
Ann Waters
BROWN, SAMUEL mmn WATERS
1841 D Quarter in BASFORD UNION COUNTIES OF NOTTINGHAM & DERBY Volume 15 Page 425
BROWN, GEORGE mmn WATERS
1843 D Quarter in BASFORD Volume 15 Page 445
BROWN, GEORGE mmn WATERS
1844 D Quarter in BASFORD Volume 15 Page 438
Kirkby in Ashfield is in Basford registration district
Edit to add
Fluffypants - Just realised did you mention you have his marriage certificate?
What was his fathers name ?