Closed between 1916 and the late 1930s
grid reference TM 028 620
The pub is shown on the 1905 OS map but seems to have disappeared by the 1969 sheet. The 1909 Rate Book has "late" added, so the pub must have closed during that book's currency, between 1916 (the last directory entry we've found so far) and the late 1930s.
The date 1701 can be seen on the wall.
It's shown on this old OS map from about the end of the 19th century, though it isn't entirely clear from the map which building was the Cock. (interactive map)
Cock fighting (usually in a pit) was probably a regular feature near here (typically organised on Shrove Tuesday and other holidays), and hence the name was widespread until it was banned in 1795.