Eileen
Here's what I've found (so far!!):
On the 1861 census: Thomas and Sarah Jane were living at 11 Brick Street, Liverpool (if you go onto Streetmap website and type this in, it appears to still stand today!). At that time they had no children and it's recorded that Sarah Jane was born in Down, Ireland.
On the 1871 census: Thomas and Sarah were living at 5 Richards Place, Toxteth Park with children:
Charlotte b: 1864 Toxteth Park, and
John b: 1870 Liverpool
On the 1881 census: Thomas and Sarah Jane were living at 34 Brighton Street, Toxteth Park with their children as above plus:
William b: 1873 Liverpool
Thomas b: 1874 Liverpool
Sarah J b: 1878 Liverpool
On the 1891 census: Thomas and Sarah with all the above children were living at 8 Blair Street, Toxteth Park and then
On the 1901 census: Thomas and Sarah (mis-transcribed!) are recorded as living at 6 Blair Street, Toxteth Park and it looks as though all the children had then left the family home.
I will keep looking to see if I can find anything further on Hugh Mitchell and report back if I have any luck.
Hope this helps.
Kay