There is a Henry Burrows / Elizabeth Eccleston marriage in 1873 at Prescot Register Office (according to Lancashire BMD).
This looks to be that couple in 1881:
http://interactive.ancestry.co.uk/75...nSearchResults
3 Old Farm, Skelmersdale, Lancashire
Henry Burrows Head Mar 32 Coal Miner Lancashire St Helens
Eliz Do Wife 31 Do Do
James Do Son 6 Scholar Do Do
Mary Alice Do Daur 1 Do Skelmersdale
Then in 1891 they have a 20-year-old son William:
http://interactive.ancestry.co.uk/65...nSearchResults
36 Marchbank Rd, Skelmersdale, Lancashire
Henry Burrows Head M 45 Coal Miner Lancashire St Helens
Elizabeth Do Wife M 42 Do Do
William Do Son S 20 Drawer in a Coal Mine Do Do
James Do Son S 16 Do Do Do
Mary Alice Do Daur S 11 Scholar Do Skelmersdale
George Do Son 8 Do Do Do
Ellen Do Daur 6 Do Do Do
Hy Do Son 4 Do Do
One of the witnesses at William Henry Eccleston and Ann Grimshaw's marriage was a James Burrows, according to Lancashire Online Parish Clerks website.
So it seems that Elizabeth Eccleston was William's mother.