Downing Street has rejected a complete ban on parents being allowed to smack their children - but a tightening of the law is being considered instead.
The new survey is likely to prompt debate
At present parents can use "reasonable chastisement" to discipline children.
But more than 200 peers and MPs want a total ban added to the Children Bill currently going through Parliament.
Tony Blair's official spokesman said the prime minister "does not believe there should be a law banning parents from smacking their children".
However government sources say they accept some parents are exploiting this defence to justify beatings.
As a result it appears Labour is prepared to offer its MPs a free vote on the tightening up of "reasonable chastisement".
The Daily Mail newspaper says the tightening could see parents who use implements to smack their children, or who smack them regularly, at risk of prosecution under the tightened laws.
Labour MP David Hinchliffe told BBC One's Politics Show that the law needed updating.
He said: "In this country at least one child a week dies at the hands of their parents or carers. Currently the law is not helpful to those child protection agencies who have the duty of ensuring children are properly protected from abuse."
But Theresa May, Tory spokeswoman for the family, said ministers should avoid "trying to tell people how to run their lives".
"We all know there is a limit beyond which parents should not go and at the point where what is reasonable control actually becomes abuse, that obviously is wrong and government and society has a right to step in at that point."
Lib Dem spokeswoman Annette Brooke said: "At least 10 other European countries have successfully introduced a ban on smacking children, and Britain should too.
"Evidence from Sweden and Germany, countries which have introduced a ban, shows that such a rule not only protects children but has also brought about a change in culture towards children."
The Children are Unbeatable Alliance is calling for a ban. The group's Sir William Utting said: "Hitting children is as unacceptable as hitting anyone else and the law should clearly say so."
A survey last month by the alliance suggested 71% of people would support a complete ban.
About 350 organisations, including NSPCC and Liberty, want to end the defence of "reasonable chastisement".
The alliance wants the Children Bill to be amended to give youngsters the same protection as adults in the home.