Hi Julie,
Given the surname of the grandparents and the way they appear on the censuses, I think that John and Frederick were the children of John Woolley and Sarah Brown, although you would need the birth, baptism or marriage records to be absolutely certain.
I have found Sarah Palmer in 1881 and 1891, so she didn't die in 1871. See -
http://newsfeed.rootsweb.com/th/read/ENG-DURHAM-YORKS/2004-12/1104522575This gives more family details
1891 census:-
Cant Clough, Worsthorne St John, Lancashire
Sarah Palmer born Monat Sorrel, Leicestershire 62
Alice Ward born Loughborough 10 - grandchild
Thomas Ward born Loughborough 7 - grandchild
1881 census:-
Loughborough
Canal Bank
Sarah Palmer 51
George Palmer 25
Anne Palmer 20
Rose Palmer 13
Next door to:-
Isaac Ward 23
Sarah Ward 22
Alice Ward
I noticed one of your posts in 2007, which confirms the following:
On the 1881 census, Thomas Palmer of Elchester (Ilchester) is a bricklayer in Alwoodley, Yorkshire.
Further down the page is his son, Thomas Palmer, who is also a bricklayer, born c1866 in Woolwich, Kent.
I have found his marriage to Mary Ellen Wadsworth in Halifax, Yorkshire, on 28th August 1886. He gives his father as Thomas Palmer a bricklayer.
In 1901, Thomas Jnr. gives his birthplace as Bromley, Kent, and has children Thomas, Leonard and Hedley.
You can find images of the marriage of Thomas to Mary Ellen, the baptisms of Thomas and Leonard and the marriages of Thomas and Leonard on Ancestry. If you have a problem with them, please let me know.
Regards,
David