Hi, Romilly,
You are looking for children with parents William and Alice Wilson born around 1860. Further to BumbleBee's note, the following MIGHT be your family -
Marriage Indexes
Surname, Forename(s); Spouse's Surname Spouse's, Forename(s); Year; Church / Register Office; Registers At Reference
WILSON, William; KAY, Alice; 1852; Prestwich, St.Mary; Bury CE18/15/389
Marriage: 6 Sep 1852 St Mary the Virgin, Prestwich, Lancashire, England
William Wilson - 23, Stonemason, Bachelor, Back Lane
Alice Kay - 21, Dressmaker, Spinster, Back Lane, Prestwich
Groom's Father: Henry Wilson, Stonemason
Bride's Father: Benjamin Kay, Publican
Witness: David Kay; Hannah Wilson
Married by Banns by: Henry Mildred Birch, Curate
Register: Marriages 1851 - 1852, Page 195, Entry 389
Source: LDS Film 2356227
Birth Indexes
Surname, Forename(s); Mother's Maiden Name; Year; Sub-District, Registers At, Reference
WILSON, Margaret Ann; KAY; 1853; Prestwich, Bury PREST/5/40
Baptism: 29 May 1853 St Mary the Virgin, Prestwich, Lancashire, England
Margaret Ann Wilson - [Child] of William Wilson & Alice
Abode: Prestwich
Occupation: Stonemason
Baptised by: H.M. Birch, Rector
Register: Baptisms 1843 - 1863, Page 260, Entry 2074
Source: LDS Film 2356183
WILSON, Mary Ellen; KAY; 1854; Prestwich, Bury, PREST/5/91
WILSON, Henry; KAY; 1856; Prestwich, Bury, PREST/6/63
WILSON, Isaac; KAY; 1859; Prestwich, Bury, PREST/7/42
WILSON, Harriet; KAY; 1861; Prestwich, Bury PREST/8/24
Baptism: 10 Mar 1861 St Mary the Virgin, Prestwich, Lancashire, England
Harriet Wilson - [Child] of William Wilson & Alice
Abode: Clayton St. Prestwich
Occupation: Stone Mason
Baptised by: S. E. Bartlet
Register: Baptisms 1843 - 1863, Page 442, Entry 3530
Source: LDS Film 2356183
WILSON, Margaret; KAY; 1863; Prestwich, Bury PREST/9/8
WILSON, Janet; KAY; 1865; Prestwich, Bury PREST/9/97
WILSON, Elizabeth Ann; KAY; 1867; Prestwich, Bury PREST/10/67
WILSON, Jane; KAY; 1867; Prestwich, Bury PREST/10/67
Baptism: 29 May 1853 St Mary the Virgin, Prestwich, Lancashire, England
Margaret Ann Wilson - [Child] of William Wilson & Alice
Abode: Prestwich
Occupation: Stonemason
Baptised by: H.M. Birch, Rector
Register: Baptisms 1843 - 1863, Page 260, Entry 2074
Source: LDS Film 2356183
There are deaths that match the above births -
Death Indexes
Surname, Forename(s); Age at Death; Year; Sub-District, Registers At, Reference
WILSON, Margaret Ann; 2; 1856; Prestwich, Bury PREST/5/35
WILSON, Henry; 1; 1857; Prestwich, Bury PREST/5/89
WILSON, Elizabeth Ann; 0; 1867; Prestwich, Bury PREST/10/13
WILSON, Jane; 0; 1867; Prestwich, Bury PREST/10/12
WILSON Margaret 5 1868 Prestwich Lancashire Bury PREST/10/92
There is a death that MIGHT be the father -
Surname, Forename(s); Age at Death; Year; Sub-District, Registers At, Reference
WILSON, William; 38; 1867; Prestwich, Bury PREST/9/96
Burial: 16 Jan 1867 St Mary the Virgin, Prestwich, Lancashire, England
William Wilson - son of Henry Wilson
Age: 38
Abode: Prestwich
Buried by: H. M. Birch, Rector
Register: Burials 1861 - 1872, Page 170, Entry 1357
Source: LDS Film 2356234
You will need to check that these match the information you have about this family,
Hope this helps
Jim Lancaster (Bury, Lancs.)