I am now updating my original post in this thread. I have now discovered that the ancestors of Alexander Charles Turner are his parents Alexander Turner and Jane Scott. Alexander Turner was born in Kircudbright Scotland. He was baptised on 28 May 1773 in New Abbey Kircudbright Dumfries. His parents were Thomas Turner and Ann Cowan. Jane Scott was born in Northumberland and I believe was baptised in Christ Church,Tynemouth, on 10th May 1762 and her parents were Edward Scott and Eleanor Bolton.
If there are any descendants of these two couples who can point me further back I would be grateful. I have now come to the conclusion that these Turners in Deptford are not related to JMW Turner! However the family story may still hold true as have another branch of Turners in London separate to the above. Will post on another thread.