Hi Anne-Elaine,
Looking at the censuses, it seems that William was actually born in Dublin, Ireland.
His family were in Islington, London in 1851 (9 children - all born in Dublin apart from one born in Liverpool). He was an Elastic Fabric Merchant.
In 1861 he was in Hackney, London with 3 of his children described as a Retired Merchant. His wife Ann J appears to have died in London in 1862 (Free BMD).
In 1871 he (widower) is in Liverpool described as a Hatters Trimmings Seller.
A family tree on Ancestry suggests his parents were John Rogerson (1774) and Mary Anne Bell(1776) both born Dublin.
If you need more detailed information please let me know.
Alan