Not sure if you're asking about the US or elsewhere here, but there's a great book about the history of this issue in the United States, Barron Lerner's One for the Road. I don't have it with me right now so can't give a super detailed answer, but basically there were small groups of people working to raise awareness about drunk driving from the 1950s-on, with people like Robert Borkenstein (the inventor of the breathalyzer) helping to make the public, police, and the government aware of the issue. It wasn't until the late 70s and early 80s, though, that drunk driving became the big issue that the public perceives it to be today - as Lerner argues, that was largely the work of anti-drunk driving groups like Remove Intoxicated Drivers (RID) and Mothers Against Drunk Driving (MADD). It happened surprisingly late.