As the 1851 Warwickshire is searchable and you have so little info I looked for them on there first.
William Stewart Head 38 Brassfounder b Birmingham
Jane Wife 42 b Birm.
William Son 14 b. Birm.
GEORGE Son 12 b. Birm
Ellen Dau. 9 b Birm.
Address C4 Woodcock St, Aston
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Mary Stocks Head 37 widow Laundress b Birmingham
WILLIAM Son 18 Scabbard maker b Birmingham
Thomas Son 12 Errand boy b. Birmingham
Emma dau. 5 b Birmingham
Eliza Meakin visitor 21 unemployed servant b America
Address Lee Banks rd, Edgbaston, Kings Norton
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Humphrey Scott Head 37 Brassfounder b Birmingham
Sarah wife 35 b Birmingham
Emma dau. 17 Button trade b Birmingham
ANN dau. 15 Button trade b. Wolverhampton,Staffs
Samuel son 11 Brassfounder b Wolverhampton
Thomas son 9 Button trade b Birmingham
Humphrey 6 son b Birmingham
Mary Ann 3 dau. b Birmingham
Walter 1 son b Birmingham
Address Smith St, Birmingham
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Now I have addresses I may be able to find the Stewarts,
& Stocks on the 1841.
I have no Staffs records to find Ann Scott & Jemima in 1841.