Hi David
That's very useful info.
I had previously thought that Margaret Caley's parents were likely to have been John Caley (1777-1856 ?), cabinet maker, and Catherine Murray/Crellin 1785-1830 (illegitimate daughter of Somerville Murray and Eleanor Crellin.) But your info says that John had died by 1854. I wonder whether we can find an exact death date for the John Caley who was the father of Matthew, Edward and Thomas in 1841, and who was in The House of Industry in 1851.
The info you've supplied about Margaret Gill is useful. Knowing that she was alive in 1851, I searched for her as Mgt Gill, but without success. Then I looked at Mgt Gill marriages and followed them up in the censuses. I'll paste in below the first "possible" candidate I've come across (Manxwoman, correct age group, spinster with a late marriage to a Manxman):
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Liverpool, England, Marriages and Banns, 1813-1921
about Margaret Gill

Name: Margaret Gill
Age: Full Age
Marriage Date: 14 Sep 1845
Parish: Liverpool, St Nicholas
Spouse's Name: William Moore
Father's Name: James Gill
Spouse Father's Name: Richard Moore
Reference Number: 283 NIC/3/32

Image shows:
WM/full age/widower/joiner/St Andrews St/father Richard Moore, tailor.
MG/full age/spinster/Peach St/father James Gill, joiner.
Witnesses: George Teare and Mary McNally.
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1851
24 Woodstock St, Liverpool
Ancestry's transcription:
Name Age Catharine Jones 46 Eleanor Jones 9 John Jones 2 Elizabeth Price 72 William Moore 58 Margaret Moore 52

notes:
Wm Moore mar lodger house carpenter b IOM
Mgt Moore mar b IOM
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This could be her:
1861
3 Pollard St, Ancoats, Manchester
Ancestry's transcription:
Name Age John McLaren 48 H Fairweather 20 Margret Moore 61
Mgt Moore wid domestic servant b Ramsey IOM.
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1871
3 Burton St, Ardwick, Lancs
Margaret Moore head wid 71 housekeeper b Ramsey IOM
living alone.
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Can't find her in 1881.
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This could be her in 1841:
28 Burlington St, Chorlton upon Medlock, Manchester
Ancestry's transcription:
Name Age Ann Hulme 70 Richard Burkley 15 Mary Clarke 20 Martha Robert 60 Margeret Gill 40
MG servant, not born in Lancs
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Unfortunately there's no evidence whatsoever that this is/isn't the mother of Elizabeth Sophia Gill.
Jean