Unite plans to hold the industrial action from July 31 to August 3.
Bank of England workers are to stage a four-day strike in a dispute over pay.
The Unite union, which represents the workforce, said its members were angry that for the second year in a row, they had been offered a pay rise that was below the rate of inflation.
The result of this year's pay award is that up to one third of the staff will get no pay rise in 2017 at all. The amount an individual will receive is then decided at the discretion of line managers, so employees could receive less than 1% and some will receive nothing at all.
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"It is nothing short of shameful that the iconic symbol of financial services in the United Kingdom is choosing to ride roughshod over the concerns of its dedicated and hardworking staff and impose this derisory pay deal".
If management fails to resolve the disagreement, Britain's biggest labour union said it will consult members in other departments at the central bank in an escalation of the plan. "The governor can no longer turn a blind eye to what is happening on his own patch".
A spokesperson for the BoE said: "The Bank has been informed of industrial action being called by Unite the Union".
Unite regional officer Mercedes Sanchez said: "The Bank of England now faces its first strike action in over 50 years when staff in vital services across the country will be taking action because of the bank's total refusal to accept that its workforce is struggling to meet their costs of living".
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