Two small children interrupted a live BBC interview on Friday - barging into the room as their father, a political science expert, discussed South Korean government, before their frantic mother dragged them away.

The clip quickly went viral, with Twitter users describing it as “the funniest thing the BBC has ever broadcast”. But some people have said a common assumption made by people sharing the video online — that the woman seen pursing the children is hired help — is racist.

Even some media misidentified Professor Robert Kelly's South Korean spouse, Jung-a Kim, as a child minder, and numerous members of the public joked that "the nanny" had probably been fired for the mishap.

But Mr Kelly's mother, Ellen, 72, has since confirmed that Ms Kim is in fact her daughter-in-law, and the two children's mother. She is reportedly a yoga teacher in South Korea, where the family live.

According to people on Twitter, the prevalence of the assumption otherwise illustrates just how pervasive racist stereotypes are, and reflects the day to day experience of many black and Asian women who are married to white men and have mixed-race children.

Blogger Phil Yu told the LA Times “people fell back on stereotypes“ when they watched the BBC video.

He said when he tweeted the video he started getting replies, predominantly from Asian people, saying: “Did you notice how many people assume that woman is the nanny?”

“That hadn't occurred to me,” he said. “It was so clearly the terrified parents.”

He added: “There are stereotypes of Asian women as servile, as passive, as fulfilling some kind of service role. People were quick to make that assumption.”

Mr Kelly, 44, a professor at Pusan National University, was speaking about the impeachment of president Park Geun-hye when his daughter Marion, four, opened the door to his study and danced in, effectively stealing the show.

She was followed shortly afterwards by her nine-month-old brother James, who rolled after his sister on a baby stroller, and then Ms Kim, who swept into the room in a panicked pursuit of the escaped children.

While her husband carried on with the interview, his wife, a yoga teacher, appeared to be doing her best not to be seen, staying low down, sweeping up the children and quickly removing them from the room. On her hands and knees, she reached back to close the door – still desperately trying to avoid the camera.

Like his wife, Mr Kelly, apparently hoped the incident would go relatively unnoticed — response to a Twitter user commenting on the clip, Mr Kelly wrote: “Is this [the] kinda thing that goes ‘viral’ and gets weird?”

Unfortunately for him, the clip has now been viewed more than 10 million times.

Meanwhile, Mr Kelly's mother said that she was probably indirectly to blame.

She and her husband, Joseph, regularly Skype her son and grandchildren, she said, and so the children probably thought it was their grandparents on the line.

"Robert usually Skypes with us from his home office, which is where he did the interview," she said.