Ed Sweeney, Bifu's general secretary, said all financial institutions down to the tiniest building society, needed to start thinking carefully about the implications on staffing levels of the move towards monetary union in Europe.
"Banks need to be addressing the issues of retraining, and redeployment of staff, before any jobs go," said Mr Sweeney.
Bifu has asked banks for their plans for Emu, but has yet to receive any definitive response.
Mr Brown told the House of Commons last week that in principle he would like to drop the pound for the euro, although he ruled out joining the single currency before the next election due in 2002. The majority of European Union countries are due to adopt the euro on 1 January 1999.
The impact of the single currency on banking jobs will be felt first in the area of foreign exchange trading and settlement. London is the biggest foreign exchange trading centre in the world, so it will feel the squeeze hardest. Even if the UK joins monetary union later, other EU countries' adoption of the euro will mean hundreds of jobs cross-trading between their currencies will disappear with the currencies themselves.
These job losses, however, will be just a fraction of the total number of employees in financial services who will face redundancy as a result of Emu. FIET, an international trades union body, estimates job losses in the sector will be at least 200,000 Europe-wide, possibly twice as many. The Boston Consulting Group, a firm of management consultants, has estimated losses of revenue to banks from reduced trading in currencies to reach as much as $5bn (pounds 3.1bn) a year. Bifu also fears banks will seek to offset the extra financial costs entailed by introducing the euro by laying off workers.
Monetary union is not the only threat to jobs in the banking sector. There is also the prospect of further, and extensive consolidation across Europe - already evident in the tie-up between Zurich Insurance and BAT's financial services division. More mergers would almost certainly trigger an increase in redundancies in the sector.
Finally, there are concerns that a single currency could revolutionise the provision of financial products.
It could become possible for customers to click on the Internet to find the lowest-cost mortgage across Europe.