They made it up. Moreover, a single limit for all doesn't make sense given what we know about alcohol metabolism.
Richard Smith, a former editor of the BMJ, was on the panel that set the UK advisory limits for alcohol consumption in 1987 and he was reported to have said the limits were made up. One currently accessible (I think the original was in the Times, currently paywalled) report tells the story like this:
Richard Smith, a member of the Royal College of Physicians working party that produced the recommendations, told the paper the limits were prompted by "a feeling that you had to say something".
He said: "Those limits were really plucked out of the air. They were not based on any firm evidence at all. It was a sort of intelligent guess by a committee."
The committee's epidemiologist had confessed that "it's impossible to say what's safe and what isn't" because "we don't really have any data whatsoever", Mr Smith said.
The former editor of the British Medical Journal said members of the working party felt obliged to produce the guidelines because of concerns over growing evidence of the chronic damage caused by heavy, long-term drinking
Read more: http://www.metro.co.uk/news/71872-government-guessed-alcohol-limits#ixzz1nbWGAoMV
Moreover, there are good reasons to doubt the wisdom of any simplistic, population-wide advice. Anecdotally the human response to alcohol varies widely. Some people get ill, some get violent, some get mellow, some seem to drink with impunity from harm. And, at least for many western populations, we know that some alcohol is good for you so recommending abstinence isn't good advice.
The human ability to metabolise alcohol depends on alcohol and aldehyde dehydrogenase enzymes which vary a lot across populations (one theory being that agriculture and the ability to make alcohol, alongside large cities where the water supply is bacteriologically suspect generates selective pressure to cope with alcohol as booze+dirty water = clean water) and within populations. Some academic reviews of this heterogeneity are here and here.
Richard Smith sums it all up in a recent BMJ blog reporting a debate on the topic he had recently participated in:
I agreed that it’s difficult to set safe limits. I remember the debate at the working party nearly 30 years ago when the epidemiologist said it was impossible to set limits because the evidence was poor. Then there are the problems that the possible consequences of alcohol are hugely varied, including both social and medical problems, people are all different in size, body composition, and responses to alcohol, and the amount of alcohol even within the same category of drinks (beer, wine, or spirits) varies considerably.
The best advice might be to find your personal tolerance and not consume beyond it, but governments sometimes don't like to trust individuals with responsibility like that.