Is this your family in 1841. Also is this birth registration that of brother Thomas with a rather unusual spelling?
MATHER, THOMAS mmn WILLOWSEE
GRO Reference: 1839 J Quarter in BOLTON UNION, COUNTY OF LANCASTER Volume 21 Page 152
Barlow Street, Bolton, Lancashire, England
John Mather 40 b Lancashire
Jane Mather 30 b Lancashire
James Mather 14 b Lancashire
William Mather 12 b Lancashire
Mary Mather 10 b Lancashire
John Mather 7 b Lancashire
Thomas Mather 2 b Lancashire
added, looking at this family in 1851 census the eldest child recorded was Mary c1833 born Preston. I believe looking at baptisms your William was born Preston, not Bolton, this might help in search.
SS