[Merry]

As your William was buried at St Peter and St Paul Ormskirk I thought it might be helpful to record other RC Hale burials at the same church. I covered 1794 to 1850:

Burial: 3 Oct 1824 St Peter and St Paul, Ormskirk, Lancs.
Mary Hale -
Age: 4
Abode: Ormskirk
Notes: R Catholic
Register: Burials 1813 - 1825, Page 270, Entry 2155
Source: LDS Film 1849664

Burial: 15 Oct 1824 St Peter and St Paul, Ormskirk, Lancs.
Samuel Hale -
Age: 33 yrs
Abode: Ormskirk
Notes: R Catholic
Register: Burials 1813 - 1825, Page 271, Entry 2162
Source: LDS Film 1849664

Burial: 25 Dec 1828 St Peter and St Paul, Ormskirk, Lancs.
Sarah Hale -
Age: 2
Abode: Ormskirk
Notes: Roman Catholic
Register: Burials 1825 - 1843, Page 87, Entry 628
Source: LDS Film 1849664

Burial: 3 Jun 1830 St Peter and St Paul, Ormskirk, Lancs.
William Hale -
Age: 2
Abode: Ormskirk
Notes: Roman Catholic
Register: Burials 1825 - 1843, Page 136, Entry 990
Source: LDS Film 1849664

Burial: 31 Dec 1831 St Peter and St Paul, Ormskirk, Lancs.
William Hale -
Age: 6 ms
Abode: Ormskirk
Notes: Roman Catholic
Register: Burials 1825 - 1843, Page 178, Entry 1330
Source: LDS Film 1849664

Burial: 10 Jun 1837 St Peter and St Paul, Ormskirk, Lancs.
Thomas Hale -
Age: 8 yrs
Abode: Ormskirk
Notes: Roman Catholic
Register: Burials 1825 - 1843, Page 361, Entry 1168
Source: LDS Film 1849664

Burial: 6 Feb 1838 St Peter and St Paul, Ormskirk, Lancs.
Samuel Hale -
Age: 14 ms
Abode: Ormskirk
Notes: Roman Catholic
Register: Burials 1825 - 1843, Page 383, Entry 1338
Source: LDS Film 1849664

Burial: 6 Jul 1840 St Peter and St Paul, Ormskirk, Lancs.
Mary Hale -
Age: 77 yrs
Abode: Ormskirk
Notes: Roman Catholic
Register: Burials 1825 - 1843, Page 462, Entry 1906
Source: LDS Film 1849664

Burial: 9 Jan 1841 St Peter and St Paul, Ormskirk, Lancs.
Charles Hale -
Age: Infant
Abode: Ormskirk
Notes: Roman Catholic
Register: Burials 1825 - 1843, Page 482, Entry 1063
Source: LDS Film 1849664

Burial: 19 Nov 1842 St Peter and St Paul, Ormskirk, Lancs.
Ellen Hale -
Age: 11 yrs
Abode: Ormskirk
Notes: Roman Catholic
Register: Burials 1825 - 1843, Page 547, Entry 1981
Source: LDS Film 1849664

Burial: 26 Aug 1850 St Peter and St Paul, Ormskirk, Lancashire, England
Ellen Hale -
Age: 1 yr
Abode: Ormskirk
Notes: Roman Catholic
Register: Burials 1846 - 1852, Page 308, Entry 2464
Source: LDS Film 1849664

After 1852 the burial register doesn't mention anyone being Catholic.

I wondered how much of a long shot it might be that Samuel Hale was a brother of your William (William and Esther seem to have named a son Samuel, aged 16 in 1841)? Also, this might be Samuel's marriage:

Marriage: 8 Jun 1824 St Peter and St Paul, Ormskirk, Lancashire, England
Samuel Hale - (X), This Parish
Mary Huyton - (X), This Parish
Witness: Elizabeth Pew, (X); George Wignall
Married by Banns by: George Whitehead Bower, Curate
Register: Marriages 1813 - 1827, Page 209, Entry 625
Source: LDS Film 1849664

In which case he only lived for a few months after the marriage.

Many of those child burials could be children of your William. Charles buried 1841 definitely is, as his birth reg has mmn Chamberlane.

So, now you might want to look for baptisms for William and Samuel at St Anne's plus baptisms for the children of your William and Esther.

Mary Hale, bur 1840, could be the mother of your William and possibly also Samuel! Should you find records that link these people, Mary's death certificate should give the name of her husband if that was known to the informant.