Speaking to Peak FM Sergeant John Booker said police treat far-right groups the same way they would IS, as they have just as much potential to lead people towards committing terrorist acts.
Booker said: “The biggest threat is very much centred on Syrian and Iraq based groups such as Islamic State however we certainly can’t ignore the right wing issues and the far right issues that do exist in our communities and are just as much of a real threat in terms of community division, hatred and deplorable acts as anything else.”
The EDL are yet to respond to a request for comment from the Huffington Post UK, but at least one person has objected to the comparison on their behalf on Twitter.
@DerbysPolice statement that EDL are as dangerous as Isis is unprofessional and wrong. Calling edl members terrorists is well out of order!— Arthur Carling (@ArthurCarling) February 18, 2016
A spokesperson for the BNP told the Huffington Post UK they would be contacting police to demand an apology, and claimed Sgt John Booker "is simply repeating spoon fed words".
"We have never burned anyone alive in a cage, we have never raped and murdered women and children and we have never beheaded anyone. We are a legal, law abiding political party. We take part in the democratic process and we stand in elections."
The comments come after the EDL complained to the BBC about it being mentioned in a television drama called 'Silent Witness', which the broadcaster describes as a crime drama "focusing on a team of forensic pathology experts and their investigations into various crimes".
"While we can appreciate the need to heighten the drama with an emotive description such as 'the murky world of hate-crime and counter-terrorism' as published in the program description published on TV Guide and numerous other websites both in the UK and abroad, there are ways to do this without attacking the English Defence League which is a legal, volunteer-led organisation," EDL chairman Alan Spence wrote to the broadcaster.
He continued: “The murky world of hate crime and counter-terrorism is a totally different world from which the EDL operates. We are no closer to that world than are UKIP, the Conservative Party or any other legal political grouping or national charity."
Spence explains that in series 19 "you clearly link us to a character who is wanted for murder".
"It is contemptuous for the BBC to imply that the English Defence League is an organization which would attract someone who would murder anyone, regardless of whether they are Muslim or not," Spence wrote.
The EDL chairman went on to explain that a character in the episode mentioned the EDL directly.
"It would have taken very little effort to invent a fictitious organisation, or even none at all, but instead your actor was directed to explicitly name the English Defence League as the 'hate-crime' organisation. We are therefore drawn to the inevitable conclusion that a deliberate decision was made to cast such aspersions on our organisation as a whole and its members individually."
Spence adds: "It will surely not have escaped the BBC’s attention that the English Defence League has an excellent reputation for non-violent behaviour and cooperation with the authorities, particularly over the past two years, in ensuring that our activities are conducted with the minimum nuisance for the local populace.
"In those rare instances when violence does occur, it is nearly always the result of extreme provocation, in defence, or the action of members of so-called anti-fascist organisations whose sole and stated purpose is to disrupt our activities and for whom violence is the means to destroy the EDL, not the unfortunate result."
Spence asked how it was that the BBC could make "such appalling insinuations against our good name and character" and demanded a public apology from the broadcaster - agreed upon first by the EDL - that would reach as wide an audience as the 'Silent Witness' programme. Legal action was also being considered, he said.
Spence: "The BBC has failed us. According to the BBC Agreement, you have a duty to ensure that the broadcast was accurate and impartial but you failed. As members of the general public and as licence payers, we expect better from the BBC but you failed."
In a reply to the EDL earlier this month the BBC complaints department said it was not responsible for how their programmes were described in billings.
Within the programme, the complaints department said there was "no direct description" of the EDL as an organisation that "condones hate crime".
The BBC explained: "The character of John Sutherland is portrayed as an intelligent man grieving for the son killed on active duty by Taliban in Helmand province. His actions are seen through this prism of grief. We wanted to explore viewpoints from opposite ends of a political spectrum as part of the discourse into terrorism. John is quickly dismissed as a murder suspect and is revealed as a key witness who helps the police track down the culprits."
The EDL then replied directing the BBC to its own website where the episode description directly names them.
It reads: "The murder of a well-known anti-fundamentalist Muslim, Amir Aziz, leads the Lyell team to question who would kill this peaceful but outspoken man. Suspicion quickly falls on a local taxi driver, revealed as a member of the English Defence League whose son was killed by a Taliban IED.”
The BBC are yet to respond to that message.
In a post detailing the exchanges on their Tumblr page the EDL wrote of the outcome thus far: "This is not what we charged them with. The negative slur, innuendo, and implications are very clear.
"The character is portrayed as a ‘member’ of the EDL even though the EDL does not have a membership. They decided to use the EDL in their program to orchestrate and embellish a manufactured disapproval by the media and political elites of this country. We expected this cursory and shallow response, but we are undeterred and unbowed."
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Derbyshire police's comments comparing the EDL to IS also follows a report earlier this month warning that the UK should prepare for "greater violence" from far-right groups - and in "extreme cases, terrorism" - in 2016, as members increasingly target British Muslims to get their message across.
The State of Hate 2015 report warned far-right groups are increasingly turning to violence, and some had been videoed training with knives and teaching members martial arts and survivalist skills.
The report by Hope not Hate found that far-right groups had increased their public profile in 2015, staging a third more demonstrations than in 2014. Last year 61 demonstrations were held, compared to 41 in 2014.
Despite the acceleration of violence, traditional far-right movements were collapsing in the UK, such as the British National Party and the EDL, the report found. The EDL has had dwindling support and public presence since Tommy Robinson quit the group in 2013.