The classic caper film starring Michael Caine and Noel Coward got more than a quarter of the votes in an online poll by the UK chain store Woolworths.
Second place went to Four Weddings and a Funeral with Oscar winner Chariots of Fire taking the bronze in third.
Other Oscar winners on the list were Bridge on the River Kwai, Gandhi and Lawrence of Arabia.
Two Scottish films made the list with Trainspotting coming in at 8 and Gregory’s Girl at 13.
Dan Jolin, Features Editor of Total Film, said: "I can understand why [The Italian Job has] been voted the best British film as it’s extremely British with football, Minis, Benny Hill and icons like Michael Caine and Noel Coward.
Nick James, editor of Sight and Sound magazine, said: "I don’t think it’s a very significant poll. When you do a poll with the general public their memories tend not to be as long as critics’ so they go for films that have a big, popular image.
Among the British classics that didn’t make the top 20 were The Third Man, Brighton Rock, The 39 Steps, Kes, Brief Encounter, Local Hero, A Clockwork Orange and The Wicker Man.
Sight and Sound voted Carol Reed’s 1949 thriller The Third Man the greatest British Film in a poll of directors, producers, actors, academics and critics.
Nick James said: "When something like The Third Man misses out it doesn’t mean that it’s not any good just that it isn’t popular enough with the general public."
The new Hollywood version of The Italian Job starring Mark Wahlberg, Charlize Theron and Ed Norton pays homage to the original but does not try to replicate it.
F Gary Grey, director of the re-make, said: "I liked a lot of things about the original. It had great style and unforgettable performances. But the film that we’ve made is for modern audiences, with updated technology."
The re-make of the Italian Job is in cinemas now.
Best of British Top 20
2.Four Weddings and a Funeral (1994)
3.Chariots of Fire (1981)
4.Lawrence of Arabia (1962)
5.The Bridge of the River Kwai (1957)
6.Bridget Jones (2001)
7.Shirley Valentine (1989)
9.Sexy Beast (2001)
10.Get Carter (1971)
11.The Full Monty (1997)
12.Monty Python’s The Life Of Brian (1979)
13.Gregory’s Girl (1980)
16.Educating Rita (1983)
17.Secrets and Lies (1995)
18.Withnail and I (1987)
19.The English Patient (1996) 20.Doctor Zhivago (1965)