I can find them on 1841 Census at Backhouse Walk, Carlisle, Cumberland England
Sarah Blair Unknown Female 50 Ireland
Sarah Blair Unknown Female 20 Ireland
James Blair Unknown Male 20 Ireland
Margaret Blair Unknown Female 15 Ireland
Hugh Blair Unknown Male 12 Ireland
William Morrison Unknown Male 2 Cumberland
Sarah (50) dies in Backhouse walk Carlisle in June 1847 says she is the widower of John and her son James was in attendance.
Is this William on 1851 census same address as 1841 census
Backhouses Walk, Carlisle, Cumberland, England
Sarah Morrison Head Married 32 Factory Ireland
William Morrison Son 12 Errand boy Carlisle, Cumberland
John Blair Nephew 9 Carlisle, Cumberland
Is this his birth entry?
MORRISON, WILLIAM MORRISON mmn IRVING
GRO Reference: 1837 S Quarter in CARLISLE Volume 25 Page 39
Digital image available cost £3
Edit
If he was Sarah illegimate son perhaps this birth entry
BLAIR, WILLIAM -
GRO Reference: 1839 M Quarter in CARLISLE Volume 25 Page 42