Hello again Sue, I have gathered together what I have on these at present, they are are not a direct line to mine but may be a distant branch further back, regards IOW.
1881 census living Newport Road Ventnor.
Barnabas Bull b.1842 Rookley Tailor
Fanny Bull b. 1842 Shanklin Laundress
Arthur Bull b.1865 Ventnor Errand Boy
Ada Jane Bull b.1868 Ventnor Scholar
Minnie Bull b.1873 Ventnor
Mark Bull b. 1877 Ventnor
William Bull b.1875
By using a bit of deduction and the IOWFHS BMD Barnabas Bull and Fanny Lock had the following children
Elizabeth Alice Bull 1864 (1881 living with Thomas and Elizabeth Mitchell described as neice)
Arthur Henry Bull 1865
Ellen Bull 1867( Death of Ellen Bull age 10 days in 1867)
Ada Jane Bull 1868
Mary Jane Bull 1870
Minnie Bull 1873
William Bull 1875
Albert Bull 1877 (is this the Mark )
Austin Edward Bull 1879(died age 5 months)
George Bull 1881
A Barnabas Bull age 8 born Carisbrooke was in the House of Industry in the 1851 census, no marriage found as yet for Barnabus and Fanny, there was a Barnabas Bull born 1842 on the island with siblings William Bull born 1840 and Maria Bull born 1844, parents not known as yet.
Fanny Lock gives her birthplace as Shanklin 1842, there are two possible , one the daughter of James Lock and Jane Lowe or William and Elizabeth King.
William Lock married Elizabeth King 1840, in the 1841 census there was a William Lock age 25 born Shanklin with wife Elizabeth 25.
They had the following children
Fanny Lock 1841
William Lock1842
Elizabeth Lock 1845
Mary Jane Lock 1847
There is a death of William Lock in 1848 age 34 and Elizabeth was a widow by the 1851 census, also listed with the other children was Emma Lock , she was an infant.
I have been able to work out that Emma Jane Mitchell born 1850 was the daughter of Elizabeth Lock nee King and Thomas Mitchell who she married in 1851,
They also had the following children.
Harriet Mitchell 1851
Robert Mitchell 1853
William John Mitchell 1855
George Mitchell 1858
Edith Mitchell 1859
Flora Mitchell 1861
Leah Mitchell 1865
If Elizabeth King/Lock/Mitchell was the aunt of Elizabeth Bull (1864) it means that James Lock and Jane Lowe were the parents of the Fanny Lock and that William and James Lock were brothers, this places them as being the sons of Maurice Lock and Ann White especially with the Shanklin connection.William Lock was born 1815 Whitwell and James was born 1820 Whitwell.
Of course you will need to check this further but I feel this is correct.