Roy,
I have an index to the 1851 Liverpool census. It does not give address or ages but I looked up the reference number for Bittern Street which is 2183.2. I then looked for james Murphy at that reference and there were 3.Here are the details:

Folio 58a
Eliza Murphy born Liverpool
Elizabeth Murphy born Liverpool
James Murphy joiner born Ireland

Folio 264
Catherine Murphy born Liverpool
Charles Murphy journeyman plasterer bornLiverpool
James Murphy born Liverpool
Margaret Murphy born Liverpool

Folio 399
Ann Murphy born Liverpool
Ann Murphy junior (2 months) born Liverpool
Charles Murphy scholar born Liverpool
Edward Murphy scholar born Liverpool
James Murphy apprentice slater born Liverpool
John Murphy apprentice slater born Liverpool
Joseph Murphy born Liverpool
Michael Murphy slater born Ireland
Thomas Murphy born Liverpool
Margaret Murphy born Wigan
Mary A born Liverpool