Right, have had a look on a*****ry for the baptism registrations for the 2 children William Arthur Blackburn and Caroline Blackburn, they are both there.
William Arthur is actually baptised William Arthur Black
MAN Turner, with a father called Albert Butt (or Bull) Turner (Laundry Proprietor) and Louisa Black
man Turner. He was baptised on 13 February 1898, with him being born on 12 January 1898. They are down as living in Chapel Street, Leeds, being baptised at St. peter's Church.
Caroline is also baptised at St. Peter's Church, this time being baptised as Caroline Blackburn on 26 July 1901, being born on 28 June 1901, just with louisa Blackburn as being her mother. She was still living at Chapel Street at this time.
I think if you were looking for William Arthur's father in the 1901 census, I would look for either an Albert Butt or Albert Bull.
Hope this helps
