bayard -
I, too associate the expression “leave go of that” with a working class accent from an industrial area of the UK, but it could also be Cockney.
A quick Google Books search shows that one Abraham Howry Espenshade in The Essentials of English Composition and Rhetoric (page 360) was saying in 1913 that ‘Leave go of, as in “Leave go of me,” is a common provincialism for let go’.
Merriam-Webster has some interesting comments to make about British and American differences over “leave go of” - most Leftpond commentators hate it, Rightponders don’t mind so much ....
The purely Cockney expression involving “leave” is “leave it out” (pronounced “aht"), meaning, normally, “kindly desist from the line of argument/behaviour you are pursuing.