Iran’s Islamic Revolutionary Guard Corps arrested the seven over anti-government protests as they tried to leave the country on Sunday, state media reported. Some of those arrested hold dual nationality.
"We are urgently seeking further information from the Iranian authorities on the reports of those British-Iranian dual nationals," British Prime Minister Rishi Sunak's spokesman said.
"We've always said that we will never accept our nationals … being used for diplomatic leverage and we urge the government of Iran to stop its practice of unfairly detaining British and other foreign nationals."
The arrests follow unrest caused by the death in detention of Mahsa Amini, 22, a Kurdish Iranian who was arrested for wearing her hijab "inappropriately".
Britain's main opposition Labour Party has asked for new sanctions to be imposed on organisations and people who have been involved in Iran's crackdown on the protests.
"The killings and repression being carried out by the Iranian regime against courageous Iranian protesters seeking a better future is appalling," Labour's foreign affairs spokesman David Lammy said.
"There must be an end to impunity."
A British Foreign Ministry representative said it had already imposed human rights sanctions on more than 40 Iranian officials and all of the "morality police".
"We will continue to hold Iran to account for the shocking violence they have inflicted on their own people," the representative said.