By campaigning since the '80s to make drink driving socially unacceptable, in the same way that smoking has become socially unacceptable.
America struggles with making drunk-driving socially unacceptable for most of the country because it is next to impossible to get public transport (which is also socially unacceptable unless you live in one of a handful of cities) or a cab unless you live close to the bars .... which is impossible/illegal in so many places because of zoning laws. Unless you live in a mobile home park, which will often have a bar within walking distance
[edit] oh, and in Britain, DUI is instant jail time. You get locked up there and then (usually overnight, unless there's an accident and other schitt involved. You have to understand that America locks up more people that any other country, so getting locked up is 'ordinary' here. Not so in Britain. Add that your license is automatically taken away if you are caught drunk driving, and your insurance costs are horrific when you get your license back. But I stand by my original comment (above) that TV and other campaigns that made DUI socially unacceptable have most likely had the biggest affect in stopping people driving while drunk in Britain.