A spokeswoman for the Army said: "Far-right ideology is completely at odds with the values and ethos of the armed forces."
In response to the story, the Commission for Countering Extremism has issued a statement praising the Army's swift response and reiterating concerns about the impact of the far right in England and Wales.
Sara Khan, Lead Commissioner for Countering Extremism, said:
"This is typical of the far right. They manipulate and exploit their way into the mainstream, often targeting the military and co-opting its symbols.
"But Tommy Robinson's attention seeking is cover for divisive anti-Muslim hatred that is causing real harm to individuals, communities and society in general.
"We have to call it out. Muslims are proudly and selflessly serving in the Armed Forces, and the Army's decisive response is to be praised.
"I am very worried about the growing impact of the far right in England and Wales. We have to strengthen our response across society.
"Firstly we need to better understand the scale, the tactics and objectives and the harms of the far right. That is why my Commission has confirmed that we will bring in academics and frontline practioners to review the threat of the far right in England and Wales."