A Selfridges shop assistant is facing possible dismissal after refusing to serve a man who was buying clothes with the leader of the English Defence League, Tommy Robinson.

The menswear assistant, who has not been named, angered Robinson after he declined to help his friend in the luxury London department store on Monday.

Robinson, a convicted criminal who leads anti-Islam protests that have often turned violent and have been marked by racist chanting, said the assistant asked his friend if he was with the EDL leader and then said "fuck off, I am not serving you".

Robinson said he had not heard the exchange directly, but immediately challenged the assistant who he assumed was a Muslim "because he had Mo on his name tag".

"You won't serve my friend because he's friends with me ... and I'm in the EDL," said Robinson, according to his own camera phone recording of the incident. "Is that what you're saying?"

The man held his hands up and tried to ignore the question, but eventually replied: "You can put me on the camera all you like but I ain't serving you", before walking off.

Selfridges said it was "very disappointed" and suspended the staff member pending an internal investigation. By way of apology, the store laid on a three-course meal for Robinson and his friend in its Hix restaurant, champagne and caviar bar, which included £25 portions of char-grilled sirloin steak and chips, and chocolate cake and ice-cream.

"We pride ourselves on making everyone welcome and endeavour to provide world-class customer service at all times," a Selfridges spokesman said. "We are taking the matter very seriously and are currently investigating it."

The worker is being represented by his union, USDAW.

Robinson said his friend was not associated with the EDL, adding that "if a Muslim was uncomfortable serving me I wouldn't have been bothered".

He said he did not want to see the shop assistant sacked but remarked that if a white shop assistant had refused to serve a Muslim he would be sacked immediately. He said he challenged the shop assistant because he felt he and his friend were the victim of double standards.

The day got worse for Robinson when he was later ejected from a Milton Keynes casino because, he believes, he is the EDL leader. He told the Guardian it is a pattern repeated in clubs and pubs in his hometown of Luton where proprietors fear his presence will attract trouble.

Formed in 2009, the EDL claims to be opposed to Islamic extremism and has held a series of protests across the UK that have led to numerous arrests for public order offences as EDL supporters clashed with anti-racism campaigners.

Robinson and an EDL colleague face charges, which they deny, of obstructing police in the course of attempting to organise a march to the site of British army soldier Lee Rigby's death.