According to the Daily Mail, more than half the population want to see numbers coming from abroad to live in Britain reduced by "a lot", the study found.
The poll, carried out for the communities department, showed that public demand for reducing immigration is overwhelming and growing.
It amounts to a warning to British Prime Minister David Cameron and Home Secretary
Theresa May that concerns over immigration -- which played a central role in last year's general election -- have not gone away and are likely to lead to voter frustration if the coalition fails to keep its promises.
Ministers have pledged to bring net migration -- the number of people added to the population by migration each year -- down to 1990s levels of under 100,000. In Labour's last year in power, net migration was 215,000.
The Communities Department Citizenship Survey -- a research project launched while
Tony Blair was prime minister -- attempts to measure "community cohesion", the daily said.
Its findings on immigration are notable because the survey was designed to ensure that ethnic minorities and Muslims were "robustly represented" among those consulted.
Some 10,000 people were questioned, but pollsters then gauged opinions from a further 5,000 ethnic minority members and 1,200 Muslims before reaching their conclusions.
The survey found that 78 percent of the population want to see immigration cut back. A quarter (24 percent) would like to see immigration reduced a little, while 54 percent said they wanted it cut "a lot". Fewer than one in five - 19 percent - said levels should stay the same. Only three people in 100 thought there should be an increase.
Andrew Green of the Migrationwatch think-tank said: "These figures are a very clear indication that, despite our economic troubles, immigration remains high among public concerns. The coalition government, and especially its Liberal Democrat members, would do well to remember that."
In April, the government will cap numbers of visas for less skilled workers from outside Europe to 21,700 for 2012, a reduction of a fifth. A consultation on how to cut numbers of student visas is under way.