I have found the burial of Anne Linacre on FindMyPast, but it isn't indexed.
The image seems to show that husband, William, was a Fisherman of Great Meols.
William's is indexed, and Anne's is on page 49 of the filmstrip.
A lot of trees have William as the son of Thomas Linacre, and Mary Hill, of Great Meolse, baptised on 6th September 1702.
However, they also have his burial as 1728, which can't be correct, and Anne's death as 1782, also not correct.
David
Indeed, I should have said the (early) burial records are not indexed/searchable on FindMyPast, though the images are very much present – for the earlier years often on the same pages as the baptisms and marriages.
I agree those trees can't be correct. I don't even see a burial record for a William Linacre in 1728. The creators/copiers of those trees are also mistaken about the parents of William Linacre, I'm pretty sure. Thomas Linacre 'of West Kirby, seaman' and Mary Hill 'of Wallasy' were married by licence on 12 Sep 1698. Mary 'wife of Thomas Linacre' is buried 04 Aug 1719, with location given as West Kirby – this is almost surely Mary Hill.
One can also find baptism records for children of a Thomas Linacre of Little Meols, whom I believe is another of the same name. His wife was Ellen 'of Little Meols', buried in 1726. There's a marriage record for Thomas Linacre and Ellen Milner dated 30 Dec 1697 at West Kirby church.
On the other hand, there are children of what seems to be a third Thomas Linacre, this one of Great Meols, baptised between 1702 to 1712. You've already mentioned them: William, Henry, Paul, and Thomas. What's more, there are two baptisms (I forget which) only a few months apart, one with father Thomas Linacre of Little Meols, the other with father Thomas Linacre of Great Meols. We should therefore conclude there were three Thomas Linacre's living in the parish at this time, one of West Kirby itself, one of Little Meols, and one of Great Meols. Our line of Linacre ancestors seem to be exclusively linked to Great Meols, at least until the late 1700s, and there's only a single baptism of a William in any case.
I'm afraid, however, that I've been struggling to find the burial records for these three Thomas Linacre's. Maybe the FamilySearch index isn't perfect? The only record for a Thomas Linacre that isn't a child (i.e., described as son of X Linacre) is the one who was buried 24 Oct 1728 and described as being of West Kirby, husbandman. This is probably the first of the three, husband of Mary Hill, though the change of occupation is a little curious. The better news is that I've found a burial record dated 24 Sep 1731 for Alice Linacre, widow, of Great Meols, whom I think would be the wife of our Thomas Linacre and the mother of William. I've not found their marriage record however.
Do please let me know if you have more luck than me finding our Thomas's burial record. Perhaps with a careful manual search.