Cohen was born in Whitechapel, East London, and grew up at 91 Ashfield Street, Whitechapel. His family was Jewish: his father, Avroam Kohen, was a Polish immigrant from Łódź who worked as a tailor, and his mother was Sime Zaremba.  He was educated at the London County Council elementary school on Rutland Street until he was aged 14 and then began his working life as an apprentice tailor to his father.

In 1917, he volunteered to join the Royal Flying Corps where he used his tailoring skills as a canvas maker for balloons and other aircraft. He served in France, and also in Egypt and Palestine. He returned to England after contracting malaria and was demobilized in 1919.

Cohen was reluctant to return to tailoring after the First World War, and he established himself as a market stall holder in Hackney, in London's East End by purchasing surplus NAAFI stock with his £30 demob money. He soon became the owner of a number of market stalls and started a wholesale business.

In 1924, he created the Tesco brand name from the initials of a partner tea supplier, T. E. Stockwell (formerly Messrs Torring and Stockwell of Mincing Lane), and the first two letters of his surname. The first two Tesco stores opened at Becontree and Burnt Oak in 1931. By 1939, Cohen owned a hundred Tesco stores. His expansion was helped by the growth of new shopping centers.

With his market experience and courage, Cohen was often the one to take that risk and he had ways of drawing a crowd. Developers became keen to help him with his start-up costs because of his ability to get people into a new center, benefiting the other shops. He expanded the company by take-overs and mergers, making it the fourth largest chain in the United Kingdom by 1968. He died on 24 March 1979 at the age of 80 in London and is buried at Willesden Jewish Cemetery.

According to en.wikipedia