Henry and his wife and children can be seen in the 1851 census living at Moreton-in-Marsh:
Collins Henry Head 44 Farm Labourer Paxford Worcestershire
Collins Ann Wife 40 Broadwell Gloucestershire
Collins John Son 15 Farm Labourer Moreton Gloucestershire
Collins William Son 13 Farm Labourer Moreton Gloucestershire
Collins Fanny Dau 10 Scholar Moreton Gloucestershire
Collins Joseph Son 8 Scholar Moreton Gloucestershire
Collins Sarah Dau 5 Scholar Moreton Gloucestershire
Collins Mary A Dau 1 Moreton Gloucestershire
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I am told by Mauri Collins, a descendant of this line of the Collins family, that Henry was the son of William Collins b.1765 at Blockley, Worcestershire, England and his wife Elizabeth Broadways. They had 4 children:
Joseph Collins b.1803 at Paxton, Worcestershire
Henry Collins b.1806 at Paxton, but died at just a few days old
Henry Collins b.1807 at Paxford
William Collins b.1809 at Paxford

Joseph Collins went on to marry a girl named Elizabeth and they had 9 children. At some point, part of this family emigrated to the USA with the current generations living in Chicago, Illinois.

Henry Collins b.1807 married Ann Harris and they had 6 children, one of whom was Frances "Fanny" who married John Edward Knibbs. Fanny emigrated with her husband to South Africa in July 1859.
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I'm also told by another descendant of Henry, a lady named Margaret Guest:
William Collins. b. 1838 Moreton in Marsh married Julia Miles b. 1830 - d 1904. They had eight children after their marriage in Middlesex London 1858. Some time later, they moved to Birmingham where they lived till their deaths. William was a policeman in the Birmingham area.
Minnie was one of the children born 1868 - d 1960 where she moved to the Isle of Wight with her daughter. Minnie married Joseph Henry Morris b. 1867 - d 1945. Minnie died aged 93 at Northwood, near Cowes, Isle of Wight, England.
Margaret is descended from Henry's son William.

Ann can be seen as a widow in 1881 living at back of High Street, Moreton in Marsh, Gloucestershire, England:
Ann COLLINS Head W Female 70 Broadwell, Gloucester, England

I'm told by Mike Collins, a direct descendant of John's, that John maried Ellen Rood in Lewisham District, in Jul-Sep 1857. John was born in Moreton-in-Marsh, Gloucestershire, England but then moved to Plumstead, Kent, England where he worked at Woolwich Arsenal for 40+ years. His wife Ellen was born in about 1836 at Deptford, Kent, England.
They had five children: John (b.1858), George (b.1860), Elizabeth (b.1866), Walter (b.1870) and Ellen (b.1874).

William was a police officer in Weston Under Penyard, Herefordshire, England at the time of the 1861 census. He was married to a girl named Julia. Beccy, a current descendant of his, believes her maiden name was "MILES".
William and Julia had 8 children in total:
Julia Margaret, abt.1859, Middlesex
Anne, abt.1860, Weston under Penyard, Herefordshire
Emily, abt.1863, Bosby, Herefordshire
Albert, abt.1864-1917, Bosby, Herefordshire
Minnie, abt.1868, Birmingham, Warwickshire
Alfred, abt.1870, Birmingham, Warwickshire
William, abt.1873, Birmingham, Warwickshire
Henry, abt.1877, Birmingham, Warwickshire
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I also learned the following from Margaret Guest who's also descended from this part of the Collins family:
William Collins. b. 1838 Moreton in Marsh, married Julia Miles b. 1830 - d 1904.
They had eight children after their marriage in Middlesex London 1858. Some time after they married they moved to Birmingham where they lived till their deaths. William was a policeman in the Birmingham area. Minnie was one of the children born 1868 - d 1960. She moved to the Isle of Wight with her daughter. Minnie married Joseph Henry Morris b. 1867 - d 1945.
Margaret is descended from Minnie.