Richard Cliff married Ellen Blackburn in 1859, Preston Register Office or Registrar Attended. So you may need to order a copy of the marriage cert to get the name of Richard's father for certain.
But this looks likely for his family in 1851:
https://www.ancestry.co.uk/interacti...=successSource
Richard Cliff Head Mar 42 Basket Maker Liverpool
Elizabeth Do Wife Mar 34 do
Richd do Son 15 Basket Maker do
Margt do Daur 6 do
Willm do Son 3 do
Benjamin do Son 6 mo do.
It looks as though Elizabeth was Richard sr's second wife - Richard Cliff married Elizabeth Burton in 1843 in Liverpool. (The GRO birth index gives Burton as Benjamin's mother's maiden name.)