Oak Street was a small street in Southwark, running from 4th to 5th Streets, just south of Bainbridge Street.
It was not covered by Francis White, and so the only listings would be those of John MacPherson in 1785 and Clement Biddle in 1791. There seems also to have been a very small or at least very unpopulated Oak Street in the Northern Liberties; name duplication occurred frequently until Consolidation in 1854. At that time very many street names were changed.
(1785) #1, Keen, John
(1785) #12, Land, Simeon
(1785) #13, Grispin, Samuel
(1785) #15, Gwinnock, William
(1785) #16, Wells, John
(1785) #17, vacant or residents would not give name
(1785) #21, Thomson, John
(1785) #22, Gardiner, Samuel
(1785) #127, Nigley, William
(1785) #141, vacant or residents would not give name
(1791) #2 Oak St. Oakley, George, labourer, Southwark
(1791) #4 Oak St., Richards, Matthew, stocking weaver, Southwark
(1791) #8 Oak St., Cook, Peter, cordwainer, Southwark
(1791) #10 Oak St., McDowell, James, porter, Southwark
(1791) #12 Oak St., Black, Benjamin, porter, Southwark
(1791) #14 Oak St., McMullen, William, cordwainer, Southwark
(1791) #14 Oak St., Mullen, William, cordwainer, Southwark
Undoubtedly the same person.
(1791) #18 Oak St., Cake, John, cordwainer, Southwark
(1791) #20 Oak St., Revoir, Santee, porter, Southwark
(1791) #22 Oak St., Morton, George, house carpenter, Southwark
It's not at all clear where this Oak Street was in the Northern Liberties, or whether a mistake might have been made, so these entries are on the same page as the Southwark ones, temporarily:
(1791) Oak St., Addis, John, house carpenter, Northern Liberties
(1791) Oak St., Millward, William, mast maker, Northern Liberties