Since your family spells the name Hollingworth, the odds are that your family comes from the northwest of England--Cheshire, Derbyshire, Lancashire, Yorkshire, Nottinghamshire. The members of the family from the south or east of England tend to spell the name Hollingsworth.
We have done a fair amount of DNA testing among the Hollingworths and Hollingsworths of the UK, and for $99US you could find out if you match anybody. We have unearthed 1 large and 2 small genetic families of Hollingworths, so that might narrow your search.
As for your specific family, what does your birth certificate tell you about your parents? You mentioned that your father was John; what was your mother's maiden name? does the certificate give their ages? Are your parents still alive? Did you ever meet any of their brothers and sisters? And would would a naval officer have been doing near Oxford at the time of your birth? Was he student there? There is a family from Lancashire that has a tradition of naval officers. Unfortunately, they tend to spell the name Hollinworth. Doug Hollingsworth