The Banking, Insurance and Finance Union (Bifu) made the decision in the wake of the strike vote last week by UNiFI, the Barclays staff association, which is planning the first walk-out in its 80-year history.
The 54,000 Barclays staff are fighting to persuade the bank to lift its 2.75 per cent pay offer.
Rob MacGregor, assistant secretary of the TUC-affiliated Bifu, said his organisation had decided to test members' opinion because "any bank which makes a profit of £1.86bn can afford a pay rise that beats inflation". The present inflation rate stands at 3.3 per cent.
Mr MacGregor said staff at Barclays, under chief executive Martin Taylor, had been forced to put up with salary increases below the inflation rate for the last four years. "The feedback from our members is that they want to take a firm stand on pay this year."
In a turnout of 27.4 per cent, around 60 per cent of members of UNiFI voted to strike, and leaders of their rival union yesterday registered their confidence that their 8,000 members at Barclays would also vote for industrial action.
A spokeswoman for Barclays pointed out that performance-related payments would take the proposed pay increase to 5 per cent on average. There was also an average £1,000 lump sum payment at the end of March as part of a profit-sharing scheme, and this was topped up by an annual pre-Christmas bonus of 2.5 per cent.
Iain MacLean, assistant general secretary of UNiFI, said he had approached management in an attempt to negotiate a new pay deal but had been rebuffed. His union is claiming a 5 per cent increase on basic salaries or £600, whichever is greater.
The strike vote by members of UNiFI is a sign of growing anger among members of previously moderate organisations in the banking industry, which have seen the value of salaries eroded and thousands of jobs lost.