The Bandbox name is thought to date from approximately 1973. But it was on the site of an older beerhouse, called the Buttermarket Tavern. It's recorded as having changed from a beerhouse license to a full one on March 6th 1961, so evidently dates from earlier than that.

Listed in Kelly's Tradefinder Directory for Ipswich in 1973 and 1975. Address listed as 46/48 Butter Market.