Government ministers were among those urging police action after demonstrators waved placards glorifying the July 7 bombings and calling for those who insulted Islam to be killed.
Home Secretary Charles Clarke told Parliament that police were conducting a "rigorous investigation" into Friday's demonstration to see if offences had been committed.
Clarke acknowledged the deep offense caused to Muslims by the cartoons, which included an image of the Prophet Muhammed wearing a bomb-shaped turban. However violence, such as that directed at European embassies in recent days, could not be justified, he said.
The government would support any action police decided to take against protesters, he said.
No arrests were made at Friday's demonstration outside the Danish embassy in London -- over cartoons first published in a Danish newspaper -- but police said they were examining video and photographic evidence.
"We are determined that this investigation will be as swift, efficient and
thorough as possible, as is reasonable for the crimes committed," Scotland Yard said.
Some protesters waved placards with slogans such as "Behead those who insult Islam" and chanted "7/7 is on the way," a reference to the July 7 suicide bombings in the British capital which killed 52 people.
Conservative Shadow Home Secretary David Davis said "direct incitements to violence" had taken place which "emphatically crossed the line" of what was acceptable, civilized behavior.
Several Muslim leaders also condemned the protesters, who they said did not represent the majority of British Muslims.
A man who dressed as a suicide bomber for the demonstration apologized for his behavior, which he acknowledged had deeply offended the families of the July 7 victims.
Omar Khayam, 22, said he had dressed that way to make the point the right to free speech did not include the right to offend.
"But by me dressing the way I did, I did just that, exactly the same as the Danish newspaper, if not worse," he said in a statement.