Closed before 1882?
30-32 High St
grid reference TL 710 745
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.
To be let and entered upon at Michaelmas next, all that ancient well known and good accustomed inn called the Cock at Mildenhall … for particulars enquire of William Elliott, the present tenant, who intends declining the public business. Ipswich Journal, 10 Aug 1782
The manor of Mildenhall – notice given that the court let and court baron of Sir Thomas Charles Bunbury, Bart, lord of said manor will be held on Thursday 12 June at sign of Cock in Mildenhall…Ipswich Journal, 7 June 1783
(Most pub, location & historic details collated by Nigel, Tony or Keith - original sources are credited)
(*** historic newspaper information from Bob Mitchell)