The building dates from the 16th century, with many subsequent alterations. It's an old coaching inn (the entrance to the courtyard can be seen in the photo between the current furniture shop and estate agent's), which closed because its business was overtaken by the nearby Bell.

Having examined all available OS maps (back as far as 1882) without finding this pub shown, it seems likely that it closed before that date.

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.