Here is the entry you are looking for, George is listed as a Servant:
Glamorgan 1861 Census
4041 1861 CENSUS OF ST.NICHOLAS & ST.LYTHANS. REF.R.G.9/4041, E.D.2.
Piece: 4041 Folio: 017 Schedule: 041
Address: ST.NICHOLAS
WRIGHT BENJAMIN HD M 61 IMPLEMENT MAKER
SFK REDGRAVE (c1800)
WRIGHT ELIZA WI M 63 -
SFK REDGRAVE (c1798)
WRIGHT WILLIAM SO M 22 IMPLEMENT MAKER
GLA ST.NICHOLAS (c1839)
WRIGHT BETSEY DL M 24 -
GLA CARDIFF (c1837)
WRIGHT - GS - 2D -
GLA ST.NICHOLAS (c1861)
TAYLOR JANE M. VR M 27 -
GLA LLANISHEN (c1834)
GREATREX ANN SV U 29 HOUSE WORK
GLA LAVERNOCK (c1832)
DAVID THOMAS SV U 55 CARTER
GLA PETERSTON (c1806)
BARKWAY GEORGE SV U 22 IMPLEMENT MAKER
SFK HOCNE[HOXNE] (c1839)
GRIFFITH PHILIP SV U 18 IMPLEMENT MAKER AP.
GLA ST.NICHOLAS (c1843)
JOHN THOMAS SV U 19 IMPLEMENT MAKER AP.
GLA ABERTHAW (c1842)
GRIFFITH WILLIAM SV U 20 IMPLEMENT MAKER AP.
GLA BONVILSTON (c1841)
LAEREY JOHN SV U 15 IMPLEMENT MAKER AP.
IRL - (c1846)
There is only one other Barkway listed in Glamorgan also with the same birthplace, she is enumerated as a Visitor:
Glamorgan 1861 Census
4038 1861 CENSUS OF CANTON NORTH. REF.R.G.9/4038, E.D.22.
Piece: 4038 Folio: 034 Schedule: 083
Address: SUFFOLK HOUSE
HERNE JAMES HD M 29 DRAPER
GLA WHITCHURCH (c1832)
HERNE ELIZABETH WI M 30 -
GLA ST.NICHOLAS (c1831)
HERNE MARY E. DA - 2 -
GLA ST.NICHOLAS (c1859)
HERNE MARGARET C. DA - 10M -
GLA LLANDAFF (c1860)
BARKWAY SOPHIA VR U 34 DRESSMAKER
SFK HOXNE (c1827)
SHEAN CATHERINE SV U 24 GENERAL SERVANT
IRL - (c1837)
THOMAS ANN SV U 16 NURSE
GLA ST.NICHOLAS (c1845)
WILLIAMS THOMAS H. NP U 15 DRAPER APPRENTICE
BRE CRICKHOWELL (c1846)
