The UK’s fabled “soft power” influencing international affairs is under threat from restrictive immigration policies, after a new survey revealed the UK has been supplanted by the US as the most popular place of education for the world’s political leaders.

The annual survey by the Higher Education Policy Institute (Hepi) found that of the current crop of presidents, prime ministers and monarchs in power in about 200 countries, 58 studied in the US and 57 in the UK – a turnaround from previous surveys in which the UK topped the chart.

Nick Hillman, Hepi’s director, said the UK risked losing valuable international influence if it allowed its immigration policies to restrict the numbers of overseas students going to British universities.

“You build up real soft power when you educate the leading lights of other countries. In the past, we have been more successful than any other country in attracting the world’s future leaders. But these new figures suggest our pole position is under threat,” Hillman said.

“To ensure this does not become a long-term trend, we need to adopt a bold educational exports strategy, remove students from the government’s main migration target and roll out the red carpet when people come to study here.

“One practical way to make all that happen would be to end the Home Office having complete control over student migration and to share it across government departments instead, as they do in other countries.”

France was in third place with 40 alumni, with the rest of the world a long way behind, including Russia with 10 and Australia at nine. In contrast, China educated just two political leaders from outside its own shores.

Shifting political sands resulted in several British-educated world leaders stepping down or being deposed, but among the newly emerging leaders were Imran Khan, the incoming Pakistan prime minister who studied at Oxford University.

Among the newcomers are Julius Maada Bio and David J Francis, the president and the chief minister of Sierra Leone, who studied at Bradford and Southampton universities respectively.

Armen Sarkissian, the president of Armenia, also joins the circle of UK-educated leaders, having studied physics as a postgraduate at Cambridge. But a controversial inclusion is Italy’s new prime minister, Giuseppe Conte, whose claim to have studied at Girton College, Cambridge, is the subject of dispute.

Syria’s brutal Bashar al-Assad remains on the list, having studied opthamology at Imperial College’s Western Eye hospital in London. A number of Gulf and Middle Eastern monarchs and heads of state are included after attending military colleges in the UK.

The Royal Military Academy Sandhurst remains one of the UK’s most popular educators of leaders from some of the world’s smallest states, ranging from Tamim bin Hamad al-Thani, the emir of Qatar, to Prince Alois, the regent of Liechtenstein, and Hassanal Bolkiah, the sultan of Brunei.

Iceland’s president Guðni Jóhannesson, a history professor elected in 2016, remains among the best-educated of those leaders who studied in the UK, with an undergraduate degree from the University of Warwick, followed by postgraduate degrees from Oxford and London universities.