If it was Ann's mother who married Mr Tute, then here is a possible candidate from Lancashire OPC:
Baptism: 7 Sep 1823 St Anne, Tottington, Lancashire, England
Ann daughter of Alice Greenhalgh, weaver, bastard,
born 20 Nov 1822
So, if anyone can find a marriage between Alice Greenhalgh and the mysterious Mr Tute, we could have our answer.
jds1949