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“Mark Carney should come to the picket lines outside this iconic British bank today and explain why hardworking men and women deserve to face years of pay cuts,” Kavanagh said.
“They are struggling to pay their bills and feed their families because the bank has unjustly imposed a below inflation or zero pay rise.
“Unite is calling on the Bank of England to come back to the negotiating table to discuss a fair pay deal for the employees.”
Around 150 people work in the three affected departments, a union spokeswoman said, although she was unable to say how many people were on strike on Tuesday.
A spokesman for the Bank of England said it has “plans in place so that all essential business will continue to operate as normal during this period”.
He said the bank was willing to talk at any time, adding that only around two percent of the workforce had been balloted for the strike.