The visa problems facing foreign academics trying to attend international conferences in the UK reveal how science could be undermined after Brexit, one of the world’s largest research funds has said.

The Wellcome Trust, which grants more than £1bn for research each year, said the immigration system was “not up to scratch” after another scientific summit in the UK was marred by the visa barriers delegates and speakers faced.

Dr Mohamed Alnor, an assistant professor of psychiatry at Sudan International University, was denied entry to the UK to attend the World Congress of Psychiatric Genetics, which ended in Glasgow last Monday, despite spending more than $2,500 (£1,890) in fees.

Chenxing Liu, a Chinese neuropsychiatrist based at the University of Melbourne, Australia, was unable to deliver a planned presentation on evolution and schizophrenia at the four-day event because he could not get a visa in time. Visa delays also prevented the attendance of Prof Bittianda Kuttapa Thelma, the head of genetics at Delhi University and one of the eminent scholars in her field.

The problems come after several foreign scholars were denied entry to a global symposium on health systems research in Liverpool earlier this month, prompting the the World Health Organization’s alarm.

Beth Thompson, Wellcome’s head of UK and EU policy, said the visa difficulties that dogged both events showed “we don’t have the immigration system we need to deliver really great science”.

A study published last month by the trust found that a quarter of African and Asian researchers encountered visa problems, at least three times more than their European peers.

Thompson said: “It is critical that we have rules that enable researchers to travel because it is a fundamental part of their jobs. And it is really important that African and Asian researchers can participate in research. If there is discrimination in the system, it’s essential that it’s addressed.”

She is worried that European academics could soon be subjected to similar levels of mistrust and bureaucracy at the hands of UK immigration officials regarding the free movement of people after Brexit.

She said: “The current system is creaking and causes problems for researchers [outside Europe] who want to travel to conferences to share their ideas, but is also a foretaste of what come could come in future if we try to expand the current system to cover citizens from countries in the European Economic Area.”

Wellcome argues that if the UK wants to retain its reputation for scientific excellence it needs to be more welcoming of foreign academics. Thompson said: “We are suggesting a reciprocal deal where researchers can continue to move as freely as possible between the EU and the UK. If we add them into the current visa system, which isn’t quick and agile, we will lose competitive edge.

“The international movement of researchers is a key foundation of how science works – it thrives on people and ideas moving. After Brexit, the government needs to consider how to deal with the movement of researchers because it is such a fundamental factor in the way good science works and is so important to retaining the UK’s strength.”

Prof Thomas Schulze, the president of the International Society of Psychiatric Genetics which hosted the Glasgow event, said questioning the visa applications of academics from poorer countries amounts to “discrimination and libel”.

Schulze, who is director of the Institute of Psychiatric Phenomics and Genomics at the Ludwig Maximilian University of Munich, said: “We want to increase the participation of people from low and middle-income countries. And it’s something that politicians say they support, but when someone wants to travel from these countries they are treated like criminals.”

Alnor said his visa application to attend the conference was rejected because he had insufficient funds in his bank account and officials were not convinced he would return after the temporary visa expired.

“I understand the UK embassy’s worry that some people misuse the system, but they make it very difficult for others. I have been prevented from attending a very important scientific meeting after paying more than $2,500,” he said.

“The sum included the cost of travelling from Khartoum to Cairo where a priority visa application can be made. The priority service and prime time appointment cost £400 alone.”

Alnor pointed out that Sudanese people do not tend to keep money in banks because of restrictions on how much cash they can withdraw.

The Home Office said it did not discuss individual cases, but insisted that all applications were considered on their individual merits.