Issuers are attempting to avoid any tax by arranging for non-European Union institutions to pay the interest on their bonds.
Market participants are warning that the proposal, which would impose a 20 per cent tax on income from savings and investments, could deprive the City of one of its most lucrative sources of revenue and cost thousands of jobs.
Cliff Dammers of the International Primary Market Association, which represents debt and equity underwriters, said: "More and more issues are being done with Swiss paying agents, or with the issuer retaining the right to move the paying agent offshore.
"The paying agent business is not very big in London, but the problem is that we could see private banking and custody business also leave the City. We expect that to happen."
Austria, whose government supports the Brussels directive, recently issued a 500m Swiss franc bond with fine print attached that allows it to circumvent imposition of a withholding tax.
Andrew Haldenby, director of studies at the Centre for Policy Studies, said: "It is often forgotten that the bond market only consists of about 10 foreign-owned banks.
"They are very footloose and will relocate to whichever regulatory regime suits them best."
There are signs that the proposed tax is already affecting London's Eurobond market. Inter-dealer brokers, who act as middle-men in Eurobond transactions between banks, report that trading so far this year has been slow.
One broker said: "Traders are unwilling to deal until the uncertainty about the withholding tax has been sorted out. A lot of brokers have missed out on their bonuses."
Mr Dammers said: "People have stayed away from new bonds, and in the last two weeks we have seen investors begin to sell the bonds which are at risk."
The withholding tax question is expected to dominate next weekend's informal Ecofin (the European Council of Finance Ministers) meeting in Dresden, which will be attended by the Chancellor of the Exchequer, Gordon Brown.
The Government, which has the right to veto, has said that it opposes the withholding tax directive in its current form.
One proposed compromise would be to exempt issues which cannot be held in units of less than 40,000 euros. That would preserve the directive's original aim, which was to clamp down on cross-border tax evasion by retail investors.