Figures released today by the Office for National Statistics show that 38% of men drank more than the four-unit limit on at least one day in the week before being interviewed.
The recommended limit for women of three units was exceeded by 29% of women on at least one day in the previous week.
The average weekly alcohol consumption was 16.8 units for men and 8.6 units for women, ONS said in the figures for 2008.
But there has been an increase in the number of people in Great Britain who have heard of daily drinking limits, from 54% in 1997 to 75% in 2009.
In England, there were 6,769 deaths related to alcohol in 2008, an increase of 24% since 2001. Almost two-thirds were from liver disease.
Jeremy Beadles, chief executive of the Wine and Spirit Trade Association, said: "Today’s Government figures confirm the continued fall in overall alcohol consumption in the UK and show that awareness of alcohol units has increased significantly since 1997.
"While we should be concerned by the rise in alcohol related-deaths, it’s clear Government efforts to combat alcohol misuse should continue to be focused on the minority of people who drink excessively, not the vast majority who enjoy a drink in moderation."
Chris Sorek, chief executive of Drinkaware, said: “It’s shocking to discover that alcohol-related deaths are again on the increase. It’s vital now, more than ever, that we act to educate people on the effects of drinking too much before more people come to harm.”