Millions of fake cigarettes enter the UK and undermine efforts to reduce smoking, warned the council.
The Councils of Herrefordshire, Lincolnshire and Durham in 2018 found illegal clusters of cigarettes behind the walls of the shops, in sweet boxes and toilets.
Fake or "bottled" tobacco products are sold on the black market to avoid paying a customs duty, the LGA said.
Illegal trade diverts £ 2.1 billion annually from taxes from HM Revenue and Customs.
In one case, Peterborough Karun Salim Ahamed was convicted last month after using fake Facebook accounts to sell illegal cigarettes in the Lincolnshire + Boston + Spalding + Skegness + Sleaford + Kirton + Heckington and others group.
Mr. Ahamed was ordered to make 200 hours of work in the community and pay 5,000 pounds.
The LGA, which represents 370 councils in England and Wales, calls on the government to increase fines and sanctions for those who are guilty of trading in counterfeit or tax-free cigarettes and tobacco.
In another court sentence in Durham Crown last week a 72-year-old man was ordered to pay a fine of £ 35,000 after trying to sell a box of 20 brass cigarettes for £ 3.50. He was caught with more than 100,000 illegal cigarettes.
In individual cases, in Herrefordshire in December, some 81,000 cigarettes from three stores were seized. On the walls and the floor of the stores, officers found a remote hiding hiding place filled with illegal tobacco.
Trading standards officials have previously discovered illegal shuttles hidden in toilet cisterns, in candy boxes, behind fans and in ceiling lamps.
Signs of Counterfeit
False or fake cigarettes are made to look like well-known brands in the UK, but they usually have foreign health recommendations without warning about the picture of the pack.
"Unpaid cigarettes" or cigarette butts are British brands that are usually imported from abroad and sold illegally.
Cigarettes and tobacco purchased in duty-free shops are for personal use only.
Simon Blackburn, Chairman of the LGA's Safer and Stronger Board, said: "The sale of cheap, illicit tobacco by unscrupulous traders in stores, private homes and social media finances organized criminal gangs and damages legitimate traders as well as easier for young people to get attached to smoking, which undermines the efforts of the councils to help people quit.
"No cigarette is good for you, but fake cigarettes contain even higher levels of cancer-causing toxins than standard cigarettes, so people have to think twice about them."