The suggestion is in response to the nationwide demonstrations carried out by anti-mass migration protesters in the wake of the deadly mass stabbing attack on school girls attending a Taylor Swift-themed dance class in Southport last week. Three of the 11 girls stabbed were killed, while two adults were injured.
The teen suspect is reportedly the son of African migrant parents, but was allegedly born in England, police said. As a result, civil unrest in the form of riots has wreaked havoc on the nation.
Speaking to Times Radio, Walney told the host that the British public "accepted an emergency two situation" and would support any "measures necessary to get this situation under control."
"Hopefully we can see this petering out now over the next few days and the extra effort which is being put on forced being able to have effect," said Walney. "But if that isn't the case, I think the British public will back further action from ministers in this emergency to get things under control."
"Back in Covid, they were prepared to back measures that were needed in that situation and I think they would take a similar approach to keeping rioters off the streets now given the scale of damage that has been done to communities," he added.
Walney later appeared on BBC's Good Morning Scotland radio show and said: "The police should be prepared to step in where they can."
"Where there is these kinds of gatherings which are just designed to be fanning the flames of violence, (they) should be stopping people gathering. People absolutely have the right to protest in this country, but they do not have the right to riot," he said.
Over the past week, anti-mass migration protesters have rioted across the country, clashing with police, smashing windows, and torching police vehicles, which has resulted in more than 100 arrests on various charges. Some of the locations that have been targeted by the rioters included a hotel housing migrants and a mosque.
Radical Islamists have formed "Muslim patrol" vigilante groups, and on Saturday, shocking video footage posted to social media showed the group hunting down and attacking anti-mass migration protesters with weapons.
