Thanks for your comments and thoughts David.
You are correct in that Barnard was a Goldsmith/Banker. He signed his apprenticeship papers at Christmas 1654 where he was apprenticed to Robert Wellstead for a period of 8 years. I have a copy of his original signed apprenticeship papers where it states that he was the son of John Turner, Clerk of Wyddial Herts.
On the completion of his apprenticeship Barnard was granted his freedom on 8 Oct 1664. He, and his friend Sam Tookey, immediately opened their own private bank, called The Fleece or Golden Fleece in Lombard Street.
Having battled the effects of the plague the following year, the great fire on London in 1666, where Lombard Street was totally decimated, and then the stop on the exchequer by Charles II - where Barnard "lent" over £16,000 to the crown - Barnard Turner remained in business throughout these turbulent years.
He was certainly a member of the Goldsmith's Livery as he was chosen to be a member of the Court of Assistants (the governing body) on 2 November 1685.
His will doesn't mention any specific property by name unfortunately but according to A2A he certainly purchased a lot of land and homes in the nor'east of Herts.
He also records that his brother William was living with him at the time of writing his will. I found the burial of William Turner at Layston not long after Barnard's death.
I don't know if this William is the same guy as Sir William Turner who was a merchant in Lombard Street where he worked from his premises called, coincidently, The Fleece.
Unfortunately, although I have a lot of information about Barnard, I am still stuck with his father John Turner.
All I have is guesswork and speculation so far but I'll keep trying

Appreciate your help
Di