Related thread here re Mary Prickett
https://www.rootschat.com/forum/index.php?topic=879131.new#newI don’t think that Peter Bamber is related to the Joseph Bamber and Mary Prickett family.
As has been pointed out, his mother’s name is Heaton.
There is a James Bamber b 1854 mmn Heaton and Joseph 1852 mmn Heaton.
1861 2710 /120/39
Everton
Joseph Bamber 37yrs b Little Eccleston
Joseph 8 yrs
James 6 yrs
Lodging with a Crone family
As mentioned already, Peter Bamber 4 yrs is with William and Catherine Bamber.
William is also born Little Eccleston.