“There are agreed national protocols to follow when incidents are reported to have happened in another country,” the police said. “As such, we will be conducting an investigation to submit to the Spanish authorities in due course.”

A spokeswoman for the police, reached by telephone on Wednesday, said that the inquiry was continuing and that no arrests had been made. The spokeswoman, who said she was not authorized to be quoted by name, declined to confirm the name of the man, whom the BBC and other British news outlets have identified.

The man started ranting at the woman, Delsie Gayle, while he was in the aisle, after he tried to get past her to sit by the window. Ms. Gayle, who has arthritis, apparently did not get up as quickly as he wanted, so he started to point his finger in her face, and she told him to stop, she said in an interview with ITV News on Monday.

The video by the fellow passenger, David Lawrence, captures the moments when the man, seated near a window, berated and bullied the woman, ordering her to move. In addition to the insults, he told her not to speak to him in a “foreign language,” though Ms. Gayle, who was born in Jamaica, was speaking English.

“I feel very low,” she said in the interview. “He paid a fare to go on holiday, I’ve paid mine, so why does he abuse me for that due to the color of my skin?”

Once the flight attendants moved the woman, the plane eventually took off from Barcelona, and the man apparently did not face any immediate consequences.

Mayor Ada Colau of Barcelona said on Facebook on Tuesday that the city would take legal action.

“Above all, we want to express our solidarity with the victim and our repudiation, not just of the racist, shameless, rude man that perpetrated this act of violence and hate, but also of the company for making the woman move seats, rather than the person guilty of the verbal attack, who deserved to be removed from the plane and taken straight to a police station,” she said.