Forty-three percent of Britons said in a poll released Wednesday that the couple should wed, compared to 32 percent who said they should not and 26 percent who did not know.
The ICM poll for The Guardian newspaper follows fevered speculation over whether Queen Elizabeth II plans to let the two marry.
Royal heirs need the monarch's OK to wed, but Charles' situation is further complicated by religious and constitutional questions.
The couple have slowly made their relationship more public they are frequently seen together at social functions, and in June Charles greeted Parker Bowles at a charity reception with a Continental kiss on each cheek.
Public approval appears to be growing. In August 1998, a year after Diana's death, 46 percent of Britons said they opposed a second marriage for Charles, and only 35 percent approved.
Even if the two eventually marry, 70 percent of those questioned in the new poll said Parker Bowles should not become queen when Charles ascends to the throne, compared to 20 percent who said she should.
Only 21 percent said their theoretical wedding should be conducted within the Church of England, while 52 percent said it should be a civil ceremony only.
A religious marriage is thought to be problematic because both are divorced. Charles who as heir to the throne is destined to head the Church of England would be free to marry in the church because his former wife, Princess Diana, is dead, but Parker Bowles' former husband is alive.
The Church of England frowns on such second marriages, but is in the process of reconsidering that policy. Last year newspapers reported that Charles was exploring the possibility of marrying in the Church of Scotland which, unlike the Church of England, is happy to marry divorcees in a religious ceremony.
Camilla met Queen Elizabeth for the first time last year at a birthday party for former King Constantine of Greece.
The poll of 1,004 people, conducted by telephone between Friday and Sunday, has a margin of error of three percentage points.
©MMI, CBS Worldwide Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press and Reuters Limited contributed to this report