The campaign group Fathers 4 Justice said police had threatened to shoot a would-be accomplice who was dressed as comic hero Batman's sidekick Robin.
Darly Westell, a spokesman for the protest group, told Reuters: "We created a diversion at the front gates of the palace to allow Batman and Robin to walk up to the side with long ladders and climb over the fence.
"Police threatened to shoot Robin unless he got down from the fence -- which we think is unacceptable because this is a peaceful, non-violent protest. But Batman was able to continue," Westell said on Monday.
The Batman protester unveiled a banner on the front of the palace saying: "Super Dads of Fathers 4 Justice fighting for your right to see your kids."
The group believes British courts are biased against fathers in child access arrangements in divorce cases.
The royal family is currently away on holiday in Scotland.
Metropolitan Police Commissioner Sir John Stevens told BBC radio the security breach was embarrassing and called for a full report.
"If it had been someone carrying a bomb and it had been assessed he had been carrying a bomb, he would have been shot," he said.
Home Secretary David Blunkett is due to make an emergency statement on the matter to the House of Commons later on Monday.
Fathers 4 Justice named the protester as Jason Hatch. He repeatedly punched the air in triumph, grinning and waving to growing crowds below.
As the sun went down he began to blow on his fingers to keep them warm.
It was the latest in a long line of stunts by the group.
The attack on Blair in parliament four months ago caused a huge security alert, closed the chamber and prompted immediate changes to access rules for the House of Commons.
Dr Magnus Ranstorp, a security and terrorism expert at St Andrews University, told Reuters: "This is almost inexcusable, given the prominence and importance of the royal family.
"This is a part of continuous security breaches, despite the clear and present danger of terrorism we are facing."
Buckingham Palace launched a major review of security after the Daily Mirror newspaper placed an undercover reporter as a palace footman ahead of U.S. President George W. Bush's state visit to Britain in November last year.
A spokesman for Blair said stunts like that on Monday did not help to solve what is a complicated issue.
"Everyone accepts that this is a very, very difficult issue but it's an issue which is complex. It involves strong emotions and huge sensitivities and therefore has to be tackled in a sensitive way," he said.
The Buckingham Palace protest coincided with the trial of a man accused of involvement in the Blair attack.
The man who threw the missiles, Guy Harrison, 36, was fined 600 pounds in May after admitting using threatening behaviour.
His alleged accomplice, Patrick Davis, 48, appeared at Bow Street magistrates court on Monday to deny the same charge.