A study published in the Lancet looked at health data from 17 million adults.
It confirmed that nearly all ethnic minority groups were disproportionally affected in the first wave in England.
In the second wave, the differences for black and mixed ethnic groups narrowed compared with white groups.
But those from an Indian, Pakistani or Bangladeshi background were even more likely to test positive, need hospital treatment and lose their lives.
"It's concerning to see that the disparity widened among South Asian groups," said Dr Rohini Mathur, assistant professor of epidemiology at the London School of Hygiene and Tropical Medicine (LSHTM) and lead author of the research.
"This highlights an urgent need to find effective prevention measures that fit with the needs of the UK's ethnically diverse population."
The study, thought to be the largest of its type, was funded by the Medical Research Council and conducted by scientists from a group of universities including LSHTM and the University of Oxford along with the National Institute of Health Research.
The team analysed medical data collected by GPs covering 40% of England and compared it with coronavirus-related data for the first and second waves of the pandemic - including testing, hospital and mortality records.
In the first wave of the pandemic, from February to September 2020, nearly every ethnic minority group in the UK had a higher relative risk for testing positive, hospitalisation and death.
The largest disparity was in intensive care admissions, which more than doubled for most ethnic minority groups compared with white groups, with black people more than three times more likely to be admitted to ICU after age and sex were taken into account.
For black and mixed groups the differences narrowed between the first and second wave from September to December for reasons that are still not fully understood. It's thought access to better testing, targeted publicity campaigns and new ways of reducing risk at work may have all played a part.
But the data shows that those from the Indian, Pakistani and Bangladeshi community were still significantly more likely to get sick, end up in hospital and die compared with those who self-reported as white.
The authors of the research said medical factors including weight, blood pressure and other underlying health conditions played the biggest role in explaining the increased risk in South Asian groups.
According to the most recent 2011 census, 21% of South Asian groups live in multigenerational households, compared with about 7% of white groups.
The report said greater household size was also an important factor in explaining the increased death rate.
"In general, living in multigenerational households and highly networked communities is of huge social benefit," said Dr Mathur at LSHTM.
"But with infectious diseases it may also increase risk of exposure to the infection from younger or working age adults who may bring the virus into the household and may potentially put older members at risk."
Based on their findings, the researchers are calling for more support to tackle what they call the structural racism faced by some communities. They said improved access to healthcare could increase the uptake of both testing and vaccination in the future.