Thank you Marion for your interest in my 'brick wall'
Your first information is indeed 'my' William, however I already have copies of the Workhouse logs showing his birth and baptism as well as a copy of his birth certificate.
William Rae mentioned in your second possible William appears not to be him. That William Rae who died 16 feb 1939 married Emily Ainsworth in 1914, two years before he was born, therefore not 'my' William.
However, I am extremely grateful for your help.
My search continues - thank you - Joan