The Department for Transport said the ban on visitors from Kenya, Bangladesh, the Philippines, and Pakistan would enter force at 0300 GMT on April 9.
This will include anyone who left the countries or transited though them in the previous 10 days.
UK and Irish nationals and those with UK residence rights travelling from those countries will have to quarantine in hotels for 10 days.
The department said the ban was over new data showing increased risks of importing coronavirus “variants of concern”.
The new rules take the total number of red-listed countries to 39.
The government said the list expansion came at a “critical time for the vaccine programme”.
The UK has given more than 31 million people, or more than 45 percent of the population, a first dose of a coronavirus vaccine.
The additional restrictions will “help to reduce the risk of new variants–such as those first identified in South Africa and Brazil–entering England”, the Department for Transport said.
The UK has set a potential May 17 date for resuming international travel, which is banned except for a few legally permitted reasons.
A taskforce set up by Prime Minister Boris Johnson is expected to propose a traffic-light system to rank countries red, green, or amber
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