Hi Kat
Some members on Rootschat will have access to Newcastle 1861 so it may be best posting a specific thread with the title 'William Hill, Newcastle, 1861 and 1871'.
What I would suggest is posting the full details of your 1901 / 1891 and 1881 findings and let people work backwards from there.
Here's the 1871 details you wanted:
HILL, at 4 No 1 Court, St James
William, Head, 42, Shoemaker, Scotland
Mary, Wife, 36, (looks like) Sower, Scotland
Michael, Son, 19, Wireworker, Scotland
David, Son, 17, Painter or Printer, Scotland
Charlotte, Daur, 12, Scholar, N-u-T
William, Son, 9, Scholar, N-u-T
Ellen, Daur, 7, Scholar, N-u-T
Charles, Son, 4, Scholar, N-u-T
John, Son, 2, N-u-T
A point re the 16 year old orphan John that's worth pondering on however - he's in a household which includes 4 joiners!
Sorry can't be more helpful
Paul