William and Elizabeth were both born at Hull where they married. Elizabeth was widowed not long after Ann was born - she married James Nelson in 1831. No burial records can be found for a William Wells of a similar age to Elizabeth in Hull/E.Yorks between 1825 and 1831. William was a mariner, so did he die at sea ? Could he have been the William Wells buried at the coastal town of West Wittering, Sussex, in 1828 ?
A William Wells (aged 51) was buried in Hull in 1826, but this is likely to be William Brown Wells, born 1874. He had married Mary Ann GOOD in 1798 and a William Good Wells, son of William & Ann, was baptised in Hull on 26 June 1800 - no doubt the son of William Brown & Mary Ann. William Good Wells, therefore, may well be our William Wells.
Another William Wells (son of William) was also baptised in Hull - on 26 Mar 1799. However, in 1817 a William Wells married Martha Ep(s)worth at Hull and an 1851 census entry shows William/Martha Wells (ages 53/57) still living in Hull.