
The Crown Prosecution Service has appealed the decision.
Hamit Coskun was initially found guilty of a religiously aggravated public order offence, having shouted "Islam is religion of terrorism" while holding the flaming copy of Islam’s Holy Book aloft outside the Turkish consulate in London in February this year.
The 51-year-old, who was backed by free speech campaigners, had his conviction overturned by Justice Bennathan last month.
The CPS said that while burning a religious text was not a criminal act, Coskun had "demonstrated hostility towards a religious or racial group, which is a crime".
In a statement, the CPS said there was "no law to prosecute people for 'blasphemy'", but added: "Our case remains that Hamit Coskun's words, choice of location and burning of the (Quran) amounted to disorderly behavior... We have appealed the decision, and the judge has agreed to state a case for the High Court to consider."
Overturning the conviction at Southwark Crown Court, Justice Bennathan said that while burning a book of such religious importance might be something "many Muslims find desperately upsetting and offensive", the right to freedom of expression "must include the right to express views that offend, shock or disturb".
He said Coskun, who is originally from Turkey, had acted alone and had not aimed his "political speech or conduct" at a person.
During Coskun's Quran desecration in Rutland Gardens, Knightsbridge, a man emerged from a nearby building and slashed at him with a large knife, later telling police he was protecting his religion.
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The attacker, Moussa Kadri, 59, was given a suspended jail sentence in September.
In a written statement after Justice Bennathan's judgment, Coskun said he had come to England "to be able to speak freely about the dangers of radical Islam" and was now "reassured that - despite many troubling developments - I will now be free to educate the British public about my beliefs".
Coskun, who is half-Kurdish and half-Armenian, was initially convicted of a religiously aggravated public order offence of using disorderly behavior "within the hearing or sight of a person likely to be caused harassment, alarm or distress".
The charge said he was motivated by "hostility towards members of a religious group, namely followers of Islam", contrary to the Crime and Disorder Act 1998 and section five of the Public Order Act 1986.
Source: Agencies