David Miliband, the British foreign minister, condemned the arrests.
"This is harassment and intimidation of a kind that is quite unacceptable. We want to see [them] released unharmed."
Al Jazeera's Jonah Hull in London, quoting British embassy officials in Tehran, said the arrests had taken place over the course of the last two weeks.
"This is a sort of running total - if you like - of a number of arrests and detentions of British embassy employees believed to be local Iranians rather than British citizens," he said.
"All of this comes off the back of two weeks of quite strident accusations against Britain with the supreme leader [Ayatollah Ali Khamenei] calling Britain 'the most evil of all western powers' in terms of its involvement and interference in Iranian affairs."
A relative of one of those detained said: "He went out yesterday morning and I have been unable to reach him since his mobile phone is switched off. Since then I have had no news of his whereabouts."
Two reformist candidates - Mir Hossein Mousavi and Mehdi Karroubi - disputed the result that gave Mahmoud Ahmadinejad, the president, a landslide re-election victory.
The outcome sparked anti-government protests that have left at least 20 people dead, though Khamenei endorsed the result.
|Britain and Iran have expelled diplomats from each other's embassies [File: AFP]
Khamenei in a televised address last week insisted the protests must stop and vowed not to give in to the protesters.
But both Mousavi and Karroubi still insist the election was marred by fraud, calling the new government "illegitimate".
They have also rejected a proposal for a recount of some ballots by the country's highest legislative body, the Guardian council.
Al Jazeera's Alireza Ronaghi in Tehran said "almost all Iranian officials among the conservative camp are criticising Western powers for interfering in Iran's affairs".
He said there were still problems with the partial counting of the votes proposed by the council.
"That's one of the problems that's outstanding ... Mir Hossein Mousavi has rejected the committee that was formed by the Guardian council saying he will only accept a committee that is independent and made up of high-ranking clerics."
The arrests of the embassy staff are likely to put further strain on relations between London and Tehran.
Last Tuesday, Gordon Brown, the British prime minister, said the UK was expelling two Iranian diplomats after Iran forced two British diplomats to leave.
Iran's foreign minister has said Tehran is considering to downgrade ties with Britain, following intelligence reports that some people with British passports were involved in post-election violence.