In the 18th century, the family name was "Cox" with the "Hippisley" (or "Ipsley" as it was often spelt) part used as an occasional middle name. Then the family was in Abingdon, Oxfordshire and the senior member, Thomas, was a sack-weaver.
At the start of the 19th century, the family moved to Stow-on-the-Wold in Gloucestershire where Thomas's son, John, was an Agricultural Labourer (1851 census). The 1850s found the family re-located again, this time to Charlton Kings, near Cheltenham and John's son, also called John, was described as a Builder on the 1881 census.
In about 1890, the family moved to Birmingham, where Joseph (born 1864) was a builder like his father. It seems that Joseph was the first to hyphenate the surname, and fix the spelling in it's current form. His son, Ralph became a jeweller, working in the Jewelry quarter of Birmingham.
The family progressively moved from Birmingham from the 1970s, to various other places in England such as Sheffield and London but still retain links there.
Finally, investigations show that there were links between individual Hippisley and Cox families in other parts of the country, but no link between those families and this one has yet been proved, and so the origin of the use of the "Hippisley" name here is still a mystery.