I have been able to trace events for six of the children (Catherine b.1814, John b.1811, Martha, Mary (b.1801), Helen (b.1806) and Thomas b.1808), but have had no luck for the other two (William b. 1810, and Robert b. 1807 (died young). This is also the point where Barbara becomes a popular first name for girls in this line. Prior to this Barbara was a very rare name for Hubbersteys.
Catherine: Catherine married a James Kenrick (Kendrick) in 1839. By the 1861 census they were living on York Street in West Derby where James was a Vinegar warehouseman. They had 5 children (John, Richard, Elizabeth, Robert, and Joseph).
The oldest son John (b.1844, d. 1893) married Jane Tyrer in 1866. At the time of the 1881 census John was also a Vinegar Warehouseman and with Jane had had 3 children (John, Robert, and Alice).
By the 1891 census Catherine and James were living with their daughter Elizabeth, son Joseph and grandson John (b. 1867) and granddaughter Alice (b.1873), apparently the children of John and Jane above.
Here is where it gets interesting. In 1898, Thomas Grundy Hubberstey (who would be the grandson of Thomas (b.1808) - see below) marries an Alice Jane Kenrick (who was the grand daughter of Catherine (b.1814).) The Alice Jane Kenrick that he marries is from Liverpool, with the same birth year as John and Jane's Alice. Or, another way of more clearly looking at it, the great grandson of Thomas and Barbara married the great granddaughter of Thomas and Barbara. Kind of a cool connection to discover.
Martha: Martha married George Clarkson in 1831 (listed as Hubbersby). I have found records of three children, Barbara (b.1835), Mary (b.1840) and William (b.1832).
Helen married a Charles Kenrick (maybe related to Catherine's husband Joseph Kenrick). They had numerous children, 8 by my count - Barbara, Thomas, Ellen, John F., Charles, Edmund, Ruth and Elizabeth.
Mary married Seth Walmsley. I have located references to two children, William and Alice.
John: John married Mary Bradley (b. 1816) in 1838 and they too had 5 children. They were Thomas (b. 1847), William Bradley (b.1843 d.1895), Barbara (b.1842), Mary (b.1854 d.1872 at age 18) and Robert (b.1852).
Daughter Barbara married a George Nurton in 1864.
Son Thomas married Jane(t)? from Scotland and had 2 children (John 1873 and Mary Agnes 1876) and likely Janet (b.1882). It looks like Thomas remarried later to an Annie (they are listed on the 1901 census as Hubberstoy). He died in 1913. His son John appears to have married a Dorothy Pym and had 2 daughters, Janet (b.1895) who appears to have married a Robert Haworth in 1916 and Ellen (b.1899), whom looks to have married Henry Holden in 1919, and one son (Thomas born. 1903). His wife Dorothy died in 1907 and John then looks to have remarried to an Ellen Taylor in 1908 and then had 2 sons, John (b.1909) and Fred (b. 1912). All 4 children born before 1911 are listed on the 1911 census, with the address as 56 Nottingham Street, Blackburn. He died in 1943, and Ellen looks to have died in 1952.
Son William Bradley was a grocer/beer retailer. He first married Elizabeth Agnes Dove with whom he appears to have had 5 children (at least 2 of whom died very young). He then married Eleanor Hartley and had one more child (Minnie). By 1901, his son Frederick (then 26) was a cotton winder living with his married sister ( Mary Bird) and her family.
Son Robert was a plumber and married a Margaret Ann Wilson in 1877. They had 4 children (Mary, John, Margaret Wilson and Robert). Son Robert was born in 1884. Robert moved to Canada and headed west, to British Columbia (BC). In Fernie, BC he married Christina Dingsdale (of St. Helen's UK) in 1909 and they had 3 children, a daughter and two sons.
Thomas: Thomas was also a butcher. He married Ann Postlewhite in 1839 and they had 4 children (Thomas, Barbara, John, and Robert). Ann died quite young (in 1855) and this meant that the family split up for a while. While Thomas married Julia Rabbitt and moved to Bury where they had 5 children, John and Robert were sent to live with relatives in Brindle. These relatives were the family of Robert and Ciciely Fazackerly. Barbara continued to live with Thomas until she married John Dickinson in 1864. Thomas eventually remarried (to a Catherine Pearson) in 1868. He died in 1876.
Son Thomas with Julia Rabbitt (from Ireland) lived in Bury. Thomas was a gardener who apparently had quite a way with orchids. By 1901, their 3 daughters were unmarried. Catherine was working as a Cotton winder, and Rose and Annie were working as ladies tailors. Their son Thomas Edmund married Anna Maria Crosby and son Richard Herbert married Jane Morris (in 1901 he was a grocer's bookkeeper).
Richard Herbert married Jane Morris in 1903 in Blackpool. They had 4 children, two of whom died in infancy, Arthur (b.1903 d.1903), Bernard (b.1913 d.1913), Alice Morris (b.1907) and Thomas (b.1904). Thomas married Jane Hunt in 1930 and they had two daughters.
Son John (b.1841, d.1885) was also a butcher. He married Mary Elizabeth Grundy (d.1901) in 1865 and had 4 children; Thomas Grundy (b.1869), Ann (b.1868), John Anselm (b.1879) and James (b.1881). It was Thomas Grundy that married Alice Jane Kenrick in 1899 (see above).
John Anselm married Agnes Snape in 1904 and they had two sons, Wilfrid (b. 1908) and John Anselm (b.1913).
Wilfrid married Edith Cooper and had a son. John Anselm married Doris (Gillette) Stones and they had 6 children, 3 sons and 3 daughters.
Son Robert married Elizabeth Kershaw (b. 1844, d.1919) in 1866 in Whittle Le woods. They initially lived with her parents at Flash Green Farm in Brindle and then moved on to Bolton sometime after 1872. They had 5 children, the first of whom, Thomas William died at the age of three. The other children were Margaret Ann, Joseph, Barbara and Thomas William.
Robert died at age 37 in 1880 and Elizabeth eventually remarried to a Ralph Whittle. Together they had another daughter, Bertha (Whittle), who eventually married a James Downey in 1923. Coincidentally or not, both Barbara and Margaret Ann also married two Whittle brothers. Barbara married Wilfrid Whittle and Margaret Ann married John Whittle.
Pictured are my Dad (Bryan), his Mom (Dorothy Pemberton), his Dad (John Robert Hubberstey) and his grandmother (Margaret Berry). This was taken around 1937.
Son Thomas William (b. 1872, d.1931) married Margaret Berry (b.1874, d.1944) and they had 5 children (Thomas William, John Robert, Margaret, Annie, and Albert). John Robert was my grandfather and he worked in a cotton mill in Bolton from the age of 12 until he finally retired at the age of 76 ... a staggering 64 years with one company. He married a Dorothy Pemberton and had 2 children (Dorothy and Bryan).
Bryan became an architect and in 1957 married Marguerite Hafner from a small village in Switzerland. Early in 1958 they moved to Montreal, Canada where they had three children.
(Pictured are, from left to right, Thomas William (my great grandfather), Dorothy May Pemberton (my grandmother), Allan McCann (husband of Annie), Annie Hubberstey, Hilda, and Albert (son of Thomas William).