It must be noted where the name of this band came from. First of all the Durutti Column (originally spelled "Durruti") was originally a group of soldiers under the leadership of anarchist revolutionary Buenaventura Durruti, which during the Spanish Civil War fought to liberate the country from Fascism. They were said to have gone "from village to village destroying the entire social structure, leaving the survivors to rebuild everything from scratch"*.

The second, and more direct, influence was a comic strip called Return of the Durutti Column, which was of course influenced by the above. Of this Vini Reilly, of the band, said in an interview with The Record Collector:

"I was always interested in the Situationists Internationale -- an anarchist group in Europe who published a book with a sandpaper cover so that it would destroy all the other books on the shelves. In the Sixties they were very radical and through their slogans, criticisms and ideas, wanted to change something. They used the title 'the Return of the Durutti Column' many times in their manifestos. So you can see that I saw the production of a very tranquil music in 1979 as an anarchic gesture!"
Reilly exhibits in that quotation the usual shallow interpretation of history and politics that most pop stars display, but if you follow some of the hard links above you'll begin to get the more detailed and accurate story.