Since he became chief executive of the charity in 2000 it has grown from a five-person organisation to a team of more than 20, with offices in London, Seattle and Sydney.
The council was set up by environmental charity WWF and corporate giant Unilever in 1996 but is now totally independent. It raises public awareness of the damage caused by over-fishing and runs a certification programme to encourage sustainability.
"It's a huge issue because demand for seafood is going up but supply is falling and there's a real danger some sea species could disappear," he says.
Day, 30, has a background in media and politics, having worked for the BBC in his gap year before Oxford and then advised a number of Conservative MPs on the left of the party. But it was his involvement in the failed attempt by Clarke to win the Tory leadership against William Hague that put him off.
"I was just tired of political campaigning and wanted to connect with real issues, and protecting the environment is one of the biggest challenges facing the world," says May.
Five years ago, after bumping into former minister John Gummer, chair of the Marine Stewardship Council, May became head of communications at the charity. A year later he became deputy chief executive and in mid-2000 chief executive.
His marketing and communications skills have been used to good effect in building the organisation's visibility, and he has attracted support from a range of high-profile figures, including Prince Charles, Tony Blair and Sainsbury's chairman Sir Peter Davis. Seafood chef Rick Stein and food critic Loyd Grossman have taken part in the charity's campaigns on over-fishing.
Raising its public profile is crucial, he says, because the charity's aim is to get shoppers to make ethical choices about the seafood they buy.
So far the charity has persuaded manufacturers to put the Marine Stewardship Council label on more than 100 products worldwide - a standard that the charity awards to fisheries that meet certain environmental standards.
The international scope of the organisation is essential, says May, because the seafood industry is global. Hence the offices in the US and Australia, which it hopes will give eco-labelling a global reach.
But to pay for all this, the charity faces a major fundraising challenge.
While it received £500,000 at its creation in seed funding, it has since then had to stand on its own two feet. It has been successful in raising funds from companies and charitable foundations, particularly in the US, but now plans to raise £10 million from new sources, such as governments, development agencies and wealthy individuals.
But he stresses that any future supporters will want to know that they are helping an organisation that is accountable and transparent - the governance structure of the council is a key element in its identity, he says.
"We deal with lots of stakeholders, including scientists, governments and the seafood industry, and all have their own interests and motivations," he says.
The challenge was to ensure that stakeholders' views could be fed into the organisation but that no single group could 'capture' the charity.
So instead of having a membership structure, the charity has an international board of trustees that is advised by a stakeholders' council of 40 people representing eight sectors. There is also a technical advisory board that advises on the standards. Both these groups elect a proportion of the full board.
When the organisation was set up, it was hoped that eventually the income generated from certification would make the charity self-financing. In practice, that is unlikely to happen, says May, as current charges for use of the council's logo are very low to encourage more fisheries to sign up.
"Our trading company should break even in a couple of years and by 2007 we hope it will be making a contribution to our other costs, but it will never fund the whole organisation because there are so many other things we want to do, such as education initiatives."
All this activity is giving May a high profile, not only in the conservation world but also in business. Last year, he was named one of the year's distinguished 100 global leaders by the World Economic Forum, an international organisation that brings together influential thinkers each year in Davos, Switzerland.
May appears embarrassed by the citation but says he enjoyed the event: "In the debates at Davos it was interesting that it was usually the corporate directors who were coming up with radical ideas on protecting the environment and it was the government ministers who were pouring cold water on them."
He argues that public distrust of government, as seen in the GM foods debate, means there is a key role to be played by non-profit organisations.
"Providing we can show our independence and scientific credibility, we can become a globally recognised body for setting standards," he says.