The Unite union said 2,400 managers will work to rule on July 15-19, followed by strike action on July 20-22.
Unite general secretary Sharon Graham said: "This business is awash with cash but it is putting profits and dividends for the few at the top ahead of its duties as a public service.
"There is not a single aspect of these cuts which is about improving customer service. They are being driven entirely by a culture of greed and profiteering which has seized a 500-year-old essential service, driving it close to ruin.
"Our members are determined to force the business to take a different path, and they have the full backing of Unite."