The couple claim they were simply holding hands while buying food after work.
It has also prompted about 200 people to take part in a “kissathon” protest at a Sainsbury’s store where they played the music of Donna Summer and Diana Ross.
The incident involved Thomas Rees, 32, and his boyfriend Joshua Bradwell, 25, being told by a security guard that a complaint had been made about the couple by another shopper.
"He waited for us to finish paying and he then beckoned us out of the store with his finger and said, 'Follow me guys,'" Rees said.
"He said he'd taken us outside so as not to embarrass us in front of the other customers.
"Well, I'm not embarrassed, I'm not ashamed - I have nothing to be ashamed of. You're not saving my dignity by taking me outside, you're just exposing your small-mindedness."
Rees added that there should be better education and training for security staff so this kind of situation does not happen again.
"All security guards in bars, restaurants, in nightclubs, supermarkets - they are the frontline for situations like this," he was quoted as saying by The BBC.
"They need to have the appropriate diversity training so they are able to handle these unique situations with a bit more respect and in a more official way than he did.
"From this security guard's point of view, he lacked the training and the experience to deal with the situation and it was his naivety that was at fault here, not any kind of prejudice."
A Sainsbury's spokesperson said there was currently an investigation occurring into the incident.
"We sincerely apologise to Thomas and Josh," Sainsbury's said in an official statement.
"We are an inclusive retailer and employer and do not tolerate discrimination in our stores.
“We will take appropriate action once we've concluded our investigation with our security contractor."
Sainsbury’s also provided biscuits for those that took part in the "kissathon", which they said was “a really great event and an important opportunity for the community to show their support”.
“We do our best to make sure everyone feels welcome in our stores but occasionally we make mistakes,” a spokesperson said.
“We are working hard to make sure lessons are learnt.”
A man has said diversity training is needed after he was told he was “inappropriately touching” his boyfriend in a Sainsbury’s store in east London.