Britain summoned the Iranian ambassador on Monday to protest the detention of London's envoy to Tehran at the weekend, the government said.
London wanted to convey its "strong objections" about the "unacceptable breach" of diplomatic protocol, Prime Minister Boris Johnson's spokesman said.
Ambassador Rob Macaire was arrested on Saturday after a demonstration that broke out at a memorial for 176 people killed when Iran's armed forces mistakenly shot down a Ukrainian plane last week.
Iranian authorities confirmed his arrest as a foreigner at "an illegal gathering" but said he was released soon after being identified. Macaire said he went to an event advertised as a vigil and left after five minutes when some people started shouting. He was arrested half an hour later.
"This was an unacceptable breach of the Vienna Convention and it needs to be investigated," the Downing Street spokesman said, referring to a 1961 international treaty that sets out protections from harassment for foreign diplomats.
"We are seeking full assurances from the Iranian government that this will never happen again.
"The Foreign Office has summoned the Iranian ambassador today to convey our strong objections." Tensions are running high in Iran and across the wider region after the US killing of a top Iranian commander and a retaliatory strike on coalition bases in neighbouring Iraq.