Heathrow Airport refused to allow additional flights from India before the country is added to the UK's travel red list.
Bosses at the airport turned down requests from four airlines over concerns about queues at passport control.
Passengers at the west London hub recently complained of lengthy immigration queues with waits of up to six hours.
India will be officially added to the red list at 4am on Friday morning after a surge in case numbers and the emergence of a new Covid-19 variant.
Britons returning after that point will be forced to quarantine in a hotel for 10 days.
Britain has detected more than 100 cases of the Indian variant, Health Secretary Matt Hancock said on Monday.
"We've made the difficult but vital decision to add India to the red list. This means anyone who is not a UK or Irish resident or a British citizen cannot enter the UK if they've been in India in the previous 10 days," Mr Hancock told parliament.
India faces a coronavirus storm overwhelming its health system, Prime Minister Narendra Modi said in a national address on Tuesday.
Health authorities there reported 314,835 new coronavirus infections on Thursday – the biggest daily rise reported in any country.
India's 2,023 deaths in one day were also its highest in the pandemic, stretching hospitals to breaking point.
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A worker serves a customer at a coffee shop in Naples, Italy, as the town is downgraded from a red to an orange zone. Reuters -
A woman wearing a protective face mask reads a book in Carignano square, Turin, Italy. EPA -
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At least 24 Covid-19 patients in western India died on Wednesday when the oxygen supply to their ventilators was disrupted, amid a nationwide shortage of the gas and a surge in infections.
Health experts said India had let its guard down when the virus seemed to be under control during the winter, allowing big gatherings such as weddings and festivals.
Mr Modi is facing criticism for addressing packed political rallies and for allowing a religious festival to go ahead where millions gathered.
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