The Campaign for Real Ale pressure group attacked the decision, saying Bass was "mercilessly stamping out hundreds of years of brewing tradition in the two cities". It said the closures could mark the end for regional beers such as Worthington Dark Mild and Hancock's HB.
The deal with Carlsberg-Tetley will mean that 537 jobs will transfer to Bass which plans to integrate the operations with its own Burton brewing capacity. Bass said the total cost of the closures would be pounds 25m, including a pounds 10m asset write-off.
Carlsberg-Tetley plans to close two other breweries in Wrexham and Alloa if a buyer cannot be found.
The dual announcements are part of the fall-out from the Government's recent decision to block Bass' planned takeover of Carlsberg-Tetley.