Frances, I should be able to help in 1841 as there is a street name. I do not have an index by name for either year, so 1851 will be more difficult, as the whole index fills four CDs. Do you have any clues as to the area in Liverpool ?
I did skip through Pitt Street in 1851 and quite by chance, I found:
HO107/2181 folio 33: entry 31
43 Cleveland Square
Henry Jennings, 29, Head, Married, Tea dealer employing 1 apprentice, b. Ireland
Lucy, wife, 27, b. Liverpool
Emily 1 1/2 ?. b. Liverpool
James 10 months b. Liverpool
Lucy Burton Matron? 87 Annuitant, b. Bury, Lancashire
Margaert Redfern Visitor Unmarried 35 Annuitant, b Bury
Elizabeth Evans 17 Unmarried House servant, b. Liverpool
Anna Minshall 13, House servant, b. Liverpool.
Iwill check 1841 later.