The research, commissioned by the Count the Casualties campaign, found that the number of British people who wanted an inquiry outnumbered those who did not by nearly four to one.
The January telephone poll conducted by Mori took a nationally representative sample of 1012 adults aged over 18. Its results were released on Wednesday.
Asked if an investigation should be held into the total number of Iraqi casualties since the 2003 invasion, 35% "strongly supported" and 24% "tended to support" the idea.
Only 15% opposed it.
Inquiry called for
The coalition of groups that commissioned the poll called on the government to order an inquiry.
"Failing to count casualties shows a fundamental disrespect for human life, allows the human cost of the invasion to grow uncontrollably and tells Iraqis that they simply don't matter," Gerard Rosenberg, director of Waging Peace, said in a statement.
"Failing to count casualties shows a fundamental disrespect for human life, allows the human cost of the invasion to grow uncontrollably and tells Iraqis that they simply don't matter"
Gerard Rosenberg, director of Waging Peace
British Prime Minister Tony Blair has previously rejected calls for an independent inquiry, saying he saw no need for one.
Any totalling of the Iraqi civilian war dead could embarrass Blair before a general election expected by May in a country that mostly opposed the war.
Blair's reputation has suffered over intelligence from British spy services used to justify the invasion of Iraq, and the subsequent failure to find any weapons of mass destruction ousted Iraqi president Saddam Hussein was said to have stockpiled.
The United States, Britain and other allies have suffered nearly 1200 deaths in combat since the invasion began.
Nearly 6400 Iraqi military deaths were recorded for 2003 while estimates by academics and peace activists, based on reports from at least two media sources, have put the civilian toll at close to 17,800 at its upper limit.
In July 2004 Aljazeera.net reported the number of Iraqi deaths to be about 37,000 during the six months between March and October 2003.
The Lancet medical journal carried a report in October in which US scientists put civilian deaths at 100,000.