A court heard Ali Mohamad and Aram Mohammedie continued to sell counterfeit products from their shop in Leeds despite repeated warnings from authorities.
A judge said the two men "flagrantly disregarded" the law by carrying out trading standards offences at the Mama Mia store on Harehills Lane.
Leeds Crown Court was told how the offending came to light on June 24, 2020.
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A police community support officer on patrol in the area became suspicious after seeing a shop assistant hide something under the counter as he was serving a customer.
The officer spoke to the assistant and then asked for the owner to be contacted,
Mohammedie spoke to the officer but denied anything illegal was being sold at the shop.
The officer then noticed a bag of illegal tobacco products hanging behind the counter.
The shop was searched by West Yorkshire Police and 2,757 illegal packets of cigarettes and 496 pouches of hand rolling tobacco were recovered.
Angus McDonald, prosecuting, said some of the products contained false Regal, Richmond, Benson & Hedges and Amber Leaf trade marks.
All of the products either failed to display a health warning or contained a health warning in a foreign language.
The court heard the defendants continued to commit similar offences despite the initial "shot across the bows".
On November 23, 2020, West Yorkshire Trading Standards arranged for a test purchase to be made at the store.
Mohamad served a test purchaser with cigarettes bearing a false Richmond trade mark.
Officers returned to the store four days later and Mohamad was behind the counter with more illegal tobacco products.
The premises were searched and 1,230 packets of cigarettes and 167 pouches of tobacco were found hidden in a store room and behind a ceiling light.
A bag containing £33,000 in cash was found in a store room on the second floor.
The products contained false Richmond, Regal, Mayfair, Golden Virginia and Amber Leaf trade marks and did not contain proper health warnings.
A further inspection took place on February 25 last year and 341 illegal tobacco products were recovered.
A trading standards test purchaser returned to the store in September and was again able to buy more fake cigarettes.
At an earlier hearing, Mohamad, 64, pleaded guilty to nine counts of possessing goods with a false trade mark for sale, one of producing or supplying a tobacco product in breach of packaging regulations and one of producing or supplying a tobacco product with a unit pack or container not carrying a combined health warning.
Mohammedie, 32, pleaded guilty to 15 counts of possessing goods with a false trade mark for sale, two of producing or supplying a tobacco product in breach of packaging regulations and two of producing or supplying a tobacco product with a unit pack or container not carrying a combined health warning.
Mohammedie pleaded guilty to a further count of selling goods with a sign or packaging bearing a sign likely to be mistaken for a registered trade mark.
Both men were due to be sentenced yesterday (January 10) but the case was adjourned by the judge, Recorder Taryn Turner, after hearing from a probation officer.
The probation officer, Mike Cooper, said Mohamad had stated in an interview that he had bought the tobacco from 'a Polish guy'.
Mr Cooper said: "He said to me that he thought the goods had come from Europe and were therefore totally legitimate."
Mohammedie also made reference to purchasing the goods from a Polish man, adding: "I thought I was getting a good deal and was not aware that they were illegal."
Both men also claimed to have medical problems.
Recorder Turner said: "In light of what I have heard, there are matters here now that have to be clarified in relation to these two defendants."
She told the pair: "It largely comes about as a consequence of what has been reported to the probation officer, which suggests that your pleas are at variance to your respective admitted involvement."
"In addition, each of you apparently have some medical ailment and conditions which your respective counsel require clarification of."
The case was adjourned until February 9. Both defendants were granted bail but were warned they face being sent to prison.
Describing the offending, Recorder Turner said: "They continued to flagrantly disregard the rules and the warnings they received."