You cannot rely on all Muslims not having alcohol. Most Muslims I know (not an unbiased sample for multiple reasons!) do drink alcohol.
Social pressure may mean people drink with friends but not in front of family or their community, or keep alcohol in their bedrooms and drink alone? Both certainly happen (no idea how much, probably varies wildly between communities).
> in my city, there is NEVER DUI accidents. We just have never heard of them
How often are drivers tested for alcohol? How good is prosecution and reporting? Can people bribe their way out if caught?
> Neither do we have alcohol overdose or an alcohol epidemic that requires assistance of alcoholic anonymous and other groups.
Again, you may the the problems but not the help because the existence of the problem is not publicly acknowledged.
It is even worse of you try to compare on a national level. There might be smuggling and home brewing.
Most importantly, any religion will cause multiple lifestyle changes. In the case of Islam some are obvious - not eating pork, Ramadan fasts, prayer times. Religious ideas change attitudes to sex, money and career, family life - pretty much your entire lifestyle.
It is even worse on a national level. A lot of differences between the US and the UK can be traced to differences in the different branches of the same religion that was dominant.
The most obvious is politics. In the 80s and 90s the largest Christian church in the UK was criticising the government for policies it regarded as not fair on the poor (welfare spending etc.) and most people belonging to the second largest voted for an outright socialist party. We do not even have a noticeable "religious right". Different from the US!
More relevant to the topic at hand is the huge and obvious difference in attitudes to alcohol. Similar differences between historically Catholic and protestant countries in Europe.