Bishop Shute Barrington was the bishop of Durham and Northumberland and also an amateur genealogist. He asked that all parish registers in Northumberland and Durham be kept in great detail. Here's a typical Bishop Shute Barrington baptism entry from Gainford parish register:
Margaret Chapman, born November 18, 1804, baptised March 31st 1805. Second daughter of John Chapman of Headlam, schoolmaster, (son of George Chapman) native of Lartington in the parish of Romaldkirk, Yorkshire, by his wife Mary Robinson (daughter of William Robinson) native of West Rounton, Yorkshire.
Bishop Shute Barrington entries affect only Northumberland and Durham for the years 1797 - 1812 but, offer valuable information and are worth looking for, even if your ancestor was born outside these dates. Look for the birth records of a sibling.
Yes I am assuming Harriet and Robert were siblings. The entry was taken from a transcript of the parish records done by Herbert Maxwell. The parishes during the Barrington years had varying manner of compliance, some had a lot of information as the above, some had less-like they may not have had the grandparent information but usually had the birth, baptism, order of birth, father's name, occupation, nativity and the same for the mother except she usually did not have an occupation.
Janis