Declaring incidents of violent disorder around the country as terrorism “has not been, and will not be, ruled out”, a police chief has warned.

It comes after director of public prosecutions (DPP) Stephen Parkinson suggested terrorism charges could be considered.

Assistant Commissioner Matt Jukes, the head of counter-terrorism policing, which is supporting forces across the country as they respond to unrest by helping with intelligence gathering and planning among other measures, said: “We know that many people will feel vulnerable at this time and we are supporting local forces with protective security expertise and advice.

“We have seen terrible examples of violent crime, disorder and criminal damage, and charges are already being brought across the country. I am very clear that using terrorism legislation or declaring activity as terrorism has not been, and will not be, ruled out.

“Counter-terrorism policing is actively assessing incidents to understand whether terrorism legislation should be applied and we will make those judgments without fear or favour.

“Our message to those involved in this disorder is; we are watching and we will not hesitate to use our powers to protect our communities.”

Mr Parkinson told the BBC on Tuesday: “Where you have organised groups planning activity for the purposes of advancing their ideology and meeting a political objective, and then planning, really, really serious disruption, then, yes, we will consider terrorism offences.”

Speaking to the PA news agency on Wednesday, he warned the publication of immigration law firms as potential targets for disorder could be considered a terrorism offence.

One case of alleged terrorism is “actively under consideration” but no such charges have yet been brought over the violence, he said.

His comments follow those earlier in the week from Neil Basu, the former head of UK counter-terrorism policing, who also suggested some of the violence being witnessed had “crossed the line into terrorism”.

But some, including one of Mr Parkinson’s predecessors, did not agree.

Lord McDonald, who was DPP between 2003 and 2008, told Times Radio rioters on the streets should be seen “as common criminals”, as he warned of the “danger” of treating them as terrorists.

He said bringing in terror legislation could be interpreted as “rather sinister” and “we should stick to conventional criminal law”.

“I think there’s a danger of aggrandising these people in some way by bringing in this sort of legislation.

“I don’t think we should see these people as terrorists. I think we should see them, as I said, as common criminals who deserve to be behind bars for rioting, for committing violent disorder, for inciting hatred and for committing criminal damage. These are conventional criminal offences that we’re all familiar with, and they are committing them in front of our eyes”, he said.

Police forces believe most of the disorder is being carried out by low-level criminals using the unrest as an excuse to commit crime and while not sophisticated, there has been some organising behind the events at a local level.

A police source said: “It’s a nuanced picture. There is a level of co-ordination, there is a level of planning.

“It’s not particularly sophisticated, there’s planning at a local level. There’s not necessarily planning by groups nationally or regionally.

“But a lot of what we’re seeing is locals reacting to what they’re seeing on social media, what they’re seeing outside in their streets, and just joining in.

“Quite a lot of forces have reported that it’s not actually right wing or left wing, sometimes a lot of it is actually just low-level criminals who they already know about joining the trouble, using it as an excuse to commit violence and looting.

“It’s a very nuanced picture, there isn’t a sort of level of sophistication that we’re seeing nationally. But, locally, there’s definitely some sort of organisation happening.”

Former prison governor Ian Acheson, an adviser to think tank the Counter Extremism Project, told the BBC he was “completely against” terrorism charges being considered.

He said: “I think giving these people an ideological justification for what they’ve done is profoundly dangerous. These are common criminals. These are people who’ve tried to incinerate human beings in hotels. They have looted vape shops, they’ve burned down libraries. There’s no ideological coherence behind any of that.

“These are common thugs, and they need to be treated as such, as they were back in 2011, and they need to be given exemplary sentences, because there’s a lot of debate to be had about the societal drivers for all of this, but for now the state has to get back in control.”