Update March 2005:

The spread of possible birth years for William Leece now spreads from 1793-1801, depnding on which source (eg death certificate, census records) is consulted.
An obvious candidate was baptised in Liverpool in December 1793, but there are several problems with this identification and it seems almost certainly the wrong man.
The 1851 census record has now been traced, also indicating born in Ireland.
Now seems his father was also William Leece, shipwright and alive in 1841. A very long shot would be that his mother was Frances Atkinson...
Ring any bells with anyone?