Under current arrangements, UK workers can choose to work longer than the maximum 48-hour working week enforced by other European countries under the directive.
However, in a non-binding vote, the European Parliament called on the European Commission to scrap the UK's opt-out.
UK business leaders have warned that an end to the UK opt-out could have a serious impact on the IT industry, which relies heavily on shift working and overtime during busy periods.
"Failure to save the opt-out will stop thousands of people from working overtime, trigger a huge rise in bureaucracy and put UK firms at a competitive disadvantage compared to EU companies," said CBI human resources policy director Susan Anderson.
But Mike Emmott, an employment relations adviser at the Chartered Institute of Personnel and Development, said EU commissioners were unlikely to approve a total ban. "There is likely to be some change, but a recent commission paper shows the EU is willing to listen to objections," he said.