Still no trace of a birth record for Henry, I did note the marriage record to Anne Lee on freereg
6 Jul 1828 in Liverpool, both single both of the parish. Henry was noted as a Carter at that time.
I note his subsequent remarriage, census records and death in 1887.
I could not find the 1841 census you mentioned but the following information may help others.
OPR on Family Search
John Ashton, age 21, of Halewood Intended marriage 25 Sep 1801 Childwall, Lancashire
To Elizabeth Lyon, age 21. They married on 1 October 1801.
John & Elizabeth of Halewood, on freereg
Margaret ASHTON Born 5 Jan 1804 Baptism 12 Feb 1804 Lancashire Huyton : St Michael
Ralph Ashton baptism 21 Apr 1811 Childwall, Lancashire, parents John & Elizabeth (family search)
1851 - Halewood, Lancashire
John Ashton 73 Farm Labourer - Bold, Lancashire
Elizabeth Ashton 73 Wife - Knowsley, Lancashire
Ralph Ashton 37 son - Halewood, Lancashire
Colin
PS The 1808 burial is on freereg.