The army is investigating after Tommy Robinson posted a video of himself with trainee soldiers who start singing his name.
The far-right activist, 35, also shared a photo of himself posing with the smiling young men on Instagram.
Robinson, real name Stephen Yaxley-Lennon, says at the start of the video: "It's the most honourable morning I've ever had anyway."
He then pans round to show the trainees, who are all wearing camouflage, as they cheer and start singing.
The English Defence League founder, who met the trainees at Watford Gap motorway services, wrote in an accompanying post: "A moment like this makes it all worth while. Today I met real British heroes."
The army said it is aware of the photograph and footage and is "investigating the circumstances surrounding this".
A spokeswoman said: "Anyone who is in breach of the army's values and standards will face administrative action.
"Far-right ideology is completely at odds with the values and ethos of the armed forces.
"The armed forces have robust measures in place to ensure those exhibiting extremist views are neither tolerated nor permitted to serve.
"Values and standards within the army play a vital role in training and development, with personnel completing annual mandatory training."
Imam Asim Hafiz, Islamic religious adviser to the armed forces, said that "any form of racism, discrimination or extremism is taken extremely seriously and will be dealt with accordingly".
He added: "The armed forces remain absolutely committed to welcoming individuals from across all faiths and cultures into its ranks."
The Muslim Council of Britain said Mr Robinson "does not represent our armed forces, however much he tries to claim otherwise".
The spokesman added: "He will rile against the very real steps taken to make the military more diverse.
"He will remain silent on the sacrifices Muslims and others made in the two world wars.
"We welcome the swift statement by the army in disassociating itself from the far-right and we hope that safeguards are put in place to ensure that Islamophobia will have no place in our armed forces."
Mr Robinson told Sky News in September that he does not care whether his message "incites fear of Muslims", as long as it "prevents children from getting raped".
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The far-right activist was found guilty of contempt of court in May last year but has been freed on bail after winning an appeal against the conviction.
Mr Robinson told Sky News: "If I believe I'm morally right then I'm not bothered about what your law says."