Britain needs to forge a deal with the European Union that brings the closest possible relationship or risk an economic downturn, the Organisation for Economic Co-operation and Development (OECD) has warned in its latest health check on the global economy.

The thinktank, which advises 34 of the world’s richest countries, appeared to support Theresa May’s deal with the EU, or an even closer alternative, as the best way to avoid harming the UK economy and placing extra strain on global growth.

The warning comes a year after the Paris-based organisation pointed out the benefits of a second referendum and a vote to remain in the EU to save the UK from a severe economic shock.

In its latest quarterly report, the OECD side-steps the potential gains from a fresh vote, but argues that the UK must maintain the highest levels of cooperation possible with Brussels.

It also repeated its warning made last year that the failure to come to a withdrawal agreement with the European Union is “by far the greatest risk in the short term”. It said a no-deal scenario could subtract more than 2% from real GDP over two years, amounting to £40bn

“Brexit is an important source of political uncertainty. It is imperative that the EU and the UK manage to strike a deal that maintains the closest possible relationship between the parties,” the OECD said.

“The lack of details on the future relationship between the United Kingdom and the European Union or the extension of the transition period, and the resulting uncertainties, could incite businesses to delay investment plans further. By contrast, prospects of maintaining the closest possible economic relationship with the European Union would lead to stronger-than-expected economic growth,” it said.

Britain’s GDP growth rate is forecast to suffer even with a Chequers-style soft Brexit, falling from 1.8% in 2016 to 1.3% this year and 1.1% in 2020. A no-deal Brexit would wreck this forecast it said, pushing growth even lower.

Brexit was one of several blows to the global economic outlook, the OECD said as it tore up its previous forecasts, saying economic storm clouds were gathering on the horizon.

Some emerging market economies that recently slipped into recession, including Argentina and South Africa, were expected to bounce back modestly in the next couple of years. But the US and Chinese economies, which have proved to be the driving force of global growth since the financial crash of 2008, are due to slow down while growth in the eurozone, Japan and Australia was also expected to falter.

“The global economy is navigating rough seas,” the OECD’s chief economist Laurence Boone said. “Global GDP growth is strong but has peaked.”

There was a sense of satisfaction, especially in the west, stemming from low levels of unemployment and low inflation, he said, but global trade and investment had been knocked by growing protectionism.

“The global economy looks set for a soft landing, with global GDP growth projected to slow from 3.7% in 2018 to 3.5% in 2019-20. However, downside risks abound and policy makers will have to steer their economies carefully towards sustainable, albeit slower, GDP growth,” he said.

In a veiled attack on the US president, Donald Trump, Boone said: “We urge policymakers to restore confidence in international dialogue and institutions. This would help strengthen trade discussions in order to tackle critical new issues and to address concerns with the rules and processes of the existing trading system.”

There was also a warning that growing inequality was hampering growth and heightening political tensions.

“Entrenched inequalities threaten growth, intergenerational mobility, and fuel discontent with the integrated global economy, which has brought prosperity across large parts of the world,” she said.

Earlier this year the OECD said it was dismayed that the recovery was being supported by low interest rates and easy credit while investment and productivity growth remained largely absent. In its latest report it said the rising cost of borrowing was potentially destabilising, especially for developing countries, and central banks needed to cooperate to limit the impact on vulnerable businesses and consumers.