Hedge fund and private equity firms surveyed about recent European Union proposals said they estimate additional regulations could cost the industry between €1.3 billion and €1.9 billion ($1.9 billion and $2.9 billion) in compliance costs for the first year alone.

The E.U. Directive envisions a system where European private investment firms would have to register in their home states, be subject to reporting requirements and maintain certain capital levels.

The survey, taken by business think tank Open Europe, included responses from 121 hedge fund and funds-of-funds managers, more than half of which are headquartered in the U.K., representing about $342 billion in assets under management. There were 41 responses from private equity managers primarily based in the U.K., whose funds totaled AUM of more than $203 billion.

U.K.-headquartered Open Europe, which has been critical of European-wide regulatory efforts in the past, said the Directive could trigger a protectionist response from non-E.U. countries, such as the U.S.

"While most of the principles behind the Directive are sound, many of the provisions in the draft Directive are overly burdensome, prescriptive, inconsistent with existing EU law or simply don't make sense,” said Mats Persson, research director at Open Europe.