The British Heart Foundation said that progress in scientific research has helped reduce fatalities to less than 2,000 in 2011.
In 2011, 1,900 people died from coronary heart disease, 1,100 men and 800 women, compared to more than 4,900 deaths in 1981.
Even though heart attack deaths are decreasing, there is little evidence that is also true of heart failure- an estimated 23,000 people are living with the condition in the region.
The most recent audit shows as many as 70% of heart failure cases are caused by coronary heart disease.
Three quarters of people with severe heart failure will not live beyond five years, according to the charity.
Heart failure occurs when so much heart muscle is damaged by the heart attack that the heart can't pump blood around the body as well as it should.
Professor Peter Weissberg, medical director, said: "It is pleasing that decades of British Heart Foundation-funded research has contributed to the dramatic fall in heart attack deaths over recent years.
"But this means that more and more people are surviving heart attacks with damaged hearts and there is now an urgent need to find ways of reversing that damage.
"Our scientists are making great strides in this fight against heart failure but success will require much more money and much more research to ensure that momentum is not lost."
The charity has launched a new media campaign to raise funds for regenerative medicine research to try and cure the condition.