Instead, the UK is supporting businesses to "do the right thing".
Recent figures show this approach is working, with more women than ever in the UK's boardrooms. Almost 16% of senior positions are now held by women, up from 12.5% last year.
May said: ?"We abandoned the last government's approach of simply trying to dictate how people should behave. ?"We are encouraging firms to use women's talents by helping them see the business benefits. But we must allow them to get on with their job.
"Our voluntary approach is reaping rewards. The past year has seen the biggest ever jump in the number of women on boards, and some of the UK's leading companies are now reporting on gender diversity, which will help more women rise to the top."
In March this year, European Union Justice Commissioner Viviane Reding launched a consultation seeking views on action at an EU-level to address the issue, including legislative measures such as introducing quotas.
The government has today written to the Commission making clear it does not support EU action in this area, backed by evidence that the number of women in senior positions can be increased without resorting to burdensome regulation.
May added: "It is particularly encouraging that this progress is being led by business, as this is the route to long term change."
The Home Secretary and Business Secretary jointly commissioned Lord Davies in August 2010 to develop a strategy to increase the number of women on the boards of UK companies.
Business secretary Vince Cable said: "Increasing the number of women on boards is not just an aspiration for greater equality; it is also an important issue for economic growth. Research shows that diverse boards make better decisions and are more effective. Since Lord Davies published his recommendations, there has been strong momentum for change and real engagement from business and investors in addressing diversity issues.??"The UK's voluntary, business-led approach, backed up by commitment from government, is achieving a culture change in a way that burdensome regulations never can, and where women take a board position based on merit rather than making up the numbers."
Research led by Cranfield School of Management shows if momentum continues, the number of women on boards will exceed Lord Davies' target of 25 per cent by 2015, and potentially reach 36.9% by 2020.