Fresh, a tobacco-control campaign in the north-east of England funded by local councils, said its research indicated that 63% of adults and more than half of retailers would support the age increase.
The charity also claimed nearly three quarters of the public (74%) said they would like to see England becoming smoke-free by 2030.
Fresh argued that the problem had become even more acute because research has indicated that the number of 18- to 34-year-olds who smoke increased by 25% during the first lockdown.
Alison Rutter, director of Fresh, said: “We need a new measures to cut smoking without delay and this is no more difficult to enforce than the law currently.
“Raising the age of sale to 21 will go a significant way towards turning off the tap of a new generation of smokers and would be no more difficult to enforce than the law now.”