Hi
I have checked the Hull personel of the 19th century but I was unable to find a Peter O`Connor,
I found a Edward Connor started 16.9,1842 and Francis O`Connor started 11.2,1879 he was PC 17
Hope this helps. I also checked the East Riding to no avail, sorry.
Rockofages
I have checked the 1861 and 1871 Census and He is definitely a policeman in both those years, there is a possibility that he could have been serving out of Hull My records could be wrong so you would be best contacting the East Yorkshire Archives in Beverley They have a very comprehensive collection of registers from the Hull city police
Rockofages