The survey of 1,000 adult smokers conducted in December found that more than 20% of adult smokers were considering buying tobacco from friends or street sellers.
Over 60% thought tobacco smuggling would get worse in the next 12 months, and 45% of smokers were aware of smuggled tobacco being sold locally.
Only one in 10 of these said they had reported such activity to the authorities.
TMA chief executive Christopher Ogden said: “The survey clearly shows that many smokers are aware of the vibrant market in illicit tobacco.
“A major concern is that the criminals making these sales don’t care who they sell to and, as a result, many under the legal age gain access to illicit tobacco.”