Another 550,000 Britons tried to quit, while 2.4 million cut back, according to the joint study by the British arm of international crawler Covid-19 from YouGov, in conjunction with the anti-smoking group Action on Smoking and Health (ASH).
The survey of 1,004 people suggested that 2% of smokers had stopped smoking due to concerns about Covid-19.
In addition, 8% of smokers said they were trying to quit, 36% said they had decreased and 27% said they were now more likely to quit.
A quarter of ex-smokers said they were now less likely to smoke again, although 4% say the pandemic has made them more prone to relapse.
The figures were received by various health and anti-smoking agencies in a statement issued by #QuitforCOVID Twitter campaign.
ASH President Nick Hopkinson, a respiratory specialist at Imperial College London, said: "Smoking damages the immune system and our ability to fight infections.
"There is growing evidence that smoking is associated with worse outcomes in patients admitted to Covid-19.
"Quitting smoking also quickly reduces people's risk of other health problems, such as heart attacks and strokes – they are bad whenever they happen, so preventing them is an end in itself, but it is especially important at a time like now , when everyone is anxious to stay out of the hospital ".
Ruth Tennant, tobacco leader for the Association of Public Health Directors, said: "There are many reasons to stop smoking, but never a more important time than now, during the coronavirus pandemic."
The founder of the #QuitforCOVID campaign on Twitter, Bristol GP Charlie Kenward, encouraged more people to stop smoking in the midst of the pandemic and beyond.
"Quitting smoking remains the biggest thing that people can do to improve their overall health," he said.
"It will improve heart and lung health, in addition to reducing the chances of developing cancer and even improving wound healing after surgery.
"There has never been a better time to give up."
The government plans to end smoking in England by 2030, as part of a series of measures to combat preventable health problems.
And the Local Government Association said the councils will play a role in helping this happen.
Community Health Council President Ian Hudspeth said: "Smokers are at particular risk of having Covid-19 and it is encouraging that many have quit the habit for good.
"Councils can help the government achieve its ambition to eliminate smoking in England by 2030, through its tobacco control and other public health and support services, but they need certainty about their long-term financing to help do it. "