Alfred Campbell consistently said he was born in Manchester in 1840. Alfred Campbell's father was a James Campbell, born in Scotland around 1808, but it has proved impossible to find where. Not only is that name too common there, there is no evidence of either of his marriages, or of the birth/baptism of Alfred.
In the 1841 census, James and his first wife (Eliza) were living at Tyrer Court, Preston Street, Liverpool, Lancs. James was a cotton spinner, and Eliza was a bonnet maker. With them was a one-year-old Alfred, but also a John Campbell, aged 15 and also born in Scotland, who could have been another son, a brother, or even a cousin.
In the 1851 census, they had moved to Catherine St, Ashton-under-Lyne, Lancs. Alfred now has a sister, Mary Ann, aged 6, but James, who was now a 'Calico Printer Journeyman', is married to a Jane Campbell rather than Eliza. It's reasonable to ask whether it's the same family.
The birth certificate for Mary says she was born 7 Sep 1844 at Hospital St, Nantwich, Cheshire. The occupation of her father (James) was 'Calico Printer' — confirming a link to the 1851 census — and the mother was Eliza Norton — confirming a link to the 1841 census. Mary Ann was baptised 16 Sep 1844 in Nantwich, Cheshire, but I could find no obvious reference to her after 1851. It turns out that Eliza had died 8 Jun 1849 at 29 Tib Street, Manchester of 'Hepatitis (6 weeks)'. The informant was James Campbell, husband, and 'Cotton Spinner'. There is no evidence of Jane's maiden name, or of their marriage.
As for the John Campbell, there's one of about the right age in the 1851 census, in the Nantwich district (Betley Street, Crewe), and lodging with the family of a John and Jane Williamson. He is married to a Margaret McJude Campbell (born 1831 in Ireland) and with a one-year-old son also called John and born in Scotland. This is interesting because there is no other mention of a Margaret McJude in Britain, either as a middle name or maiden name, and no associated marriage could be found. Jane Williamson was also born in Ireland and so Margaret may have been a relation.
Sometime between 1851 and 1860 James and Alfred moved to East London. It's difficult to say whether Jane moved with them and then back again, or stayed put, but she appears to still be in Manchester in 1861. James died 5 Jul 1860 at 8 Cropley Terrace, Hoxton New Town, Shoreditch, aged 54 of 'Pleurisy'. He was recorded as 'Musician' and his son was present at the death.
In the 1861 census, there's a Jane Campbell, occupation 'Warper', lodging at 17 Nuttal Street, Chorlton Upon Medlock, Manchester, and recorded as a widow (James had only died the previous year). In the 1871 census, this Jane is at the Chorlton Union Workhouse, Didsbury, Lancs. Again, she is recorded as a widow, with an occupation of 'Genl. Warper'. This Jane died 2 Feb 1875 in Chorlton district aged 61 of 'Phthisis' . Her address was Union Workhouse, Withington, and her occupation was 'Charrer' (probably misspelling of 'charer', as in 'charwoman'). If this is the correct Jane then she was born c1813 in Ayrshire, Scotland.
Alfred married Eliza Jane Hulme (born 3 Feb 1845 in Cripplegate, London) on 11 Nov 1860 in the parish of St. Leonard, Shoreditch. Alfred was living at 8 Cropley Terrace at the time, and Eliza at 12 Bristow St. Both Alfred and his deceased father (James) were recorded as 'Musician', and Eliza's father, John (also deceased), was recorded as a 'Modeller'.
In the 1861 census, the newly married couple were living at 18 Park Terrace, Rotherhithe, London. Both had a recorded occupation of 'Teacher of Music'. Their first-born, Eliza Amelia, was born 23 Mar 1862 at 12 Bristow St., Hoxton New Town, Shoreditch. Alfred was recorded as 'A Musician'. They then had a son, Alfred James, on 22 Sep 1863 while still at 12 Bristow St. Again, Alfred was recorded as 'Musician'.
Eliza Amelia died in 1864 in Shoreditch, aged only 2.
Annie Beatrice was born 8 Sep 1865 at 22 Cavendish St, Hoxton New Town. Alfred's occupation: 'A Musician'.
Katie Jane was born 3 Jul 1868 at 22 Cavendish St., and Alfred's occupation was recorded as 'A Musician'.
Alfred James died on 27 Feb 1869 aged 5 at 22 Cavendish St of 'Necrotis of knee joint, asthenia'. His father was in attendance.
In the 1871 census, they were living at Curzon St, St. Leonard, Shoreditch, and Alfred was now a 'Professional singer'.
Ada Florence was born 10 Mar 1875 at 12 Bristow St., Hoxton New Town — did they move back to this address? — and Alfred's occupation was now 'Vocalist'.
Around 1875, Alfred and Eliza took their remaining children (Annie Beatrice, Katie Jane, and Ada Florence) to Jersey, maybe to escape the squalour of London's East-end. Joseph Bazalgette's London sewer system was authorised in 1858 — the year of the "Great Stink" owing to the exceptional temperatures acting on the raw sewage in the Thames — and begun in 1859. It was almost completed by 1866, but not yet protecting East London. In June of that year, a cholera outbreak, traced to illegally sourced water by the East London Water Company, claimed 5,596 lives there. The sewer system was eventually finished in 1875.