Thomas Rees and Joshua Bradwell were in the shop when a security guard escorted them out, explaining a woman had complained about their behaviour.
Mr Rees told the BBC they had been holding hands and that he may have put an arm around his partner's waist.
The story caught wind online after Mr Rees expressed his disappointment at the UK supermarket giant on Twitter.
He told the BBC the incident "knocked me for six", but since the incident they had received messages of support from around the world.
