Downing Street said on Wednesday that the practice should not be used to obtain "diplomatic leverage".
Iran’s Revolutionary Guards arrested the seven people over anti-government protests as they tried to leave the country on Sunday, according to a statement published by state media. All seven had links to the UK, the Revolutionary Guards said.
“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 spokesperson told reporters.
“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 reported arrests follow unrest triggered by the September 16 death in detention of Mahsa Amini, a 22-year-old Kurdish Iranian who was arrested for wearing "inappropriate attire" under Iran's strict Islamic dress code for women.
The protests have posed one of the biggest challenges to the Shi'ite Muslim-ruled Islamic Republic since the 1979 revolution.
The Labour Party has asked for new sanctions on organisations and individuals 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 in a statement.
“There must be an end to impunity.”
Asked about the potential for future sanctions on Iran, a British foreign ministry spokesperson said it had already imposed human rights sanctions on more than 40 Iranian officials and the entirety of the so-called “morality police".
“We will continue to hold Iran to account for the shocking violence they have inflicted on their own people,” the spokesperson said.