Sources said that the Foreign Office’s minister for the Middle East Dr Andrew Murrison is having “senior-level talks with his counterpart and other officials”.
News of the mission to the Islamic Republic came as it emerged Iran executed a former defence ministry employee accused of spying for the US.
US State Department sources have warned the threat of military confrontation will not subside while Donald Trump pursues his policy of “maximum pressure” of economic sanctions, aimed at striking a comprehensive deal with the regime.
Last month Congress was told that pressure is having an effect in Iran, with funding to sections of the military being slashed.
This, they say, leaves Tehran waiting to see whether the US president secures a second Oval Office term next year.
Last week, both countries seemed to have their “Cuban missile crisis” moment after the downing of a US Global Hawk surveillance drone over international waters near Iran.
Mr Trump confirmed he came within “10 minutes” of authorising a strike on Iranian facilities but called it off after learning there would be 150 casualties.
He later clarified that the carrier-borne aircraft were within two hours of launching.
Last night Tehran said it had executed ex-aerospace technician Jalal Hajizavar for spying.
It follows recent claims that the Islamic Republic disrupted a “major CIA ring” of sympathetic cyber spies operating from within Iran and other countries.
Next month, President Hassan Rouhani’s Iran is expected to exceed the enriched low-grade uranium it is allowed under the terms of the JCPOA, the Iran nuclear deal, from which Mr Trump withdrew after assuming office.
Britain still ostensibly backs the deal, along with China, France, Germany and Russia, but privately, diplomats say the US pull-out has left it defunct.
On Friday, Mr Trump blamed the current situation with Iran on decisions by his predecessor, Barack Obama, to ratify that deal, claiming it “gave them $150billion, and $1.8billion in actual cash, and a free path to nuclear weapons”.
He tweeted that following the drone attack, he had been “cocked and loaded” and within 10 minutes of launching strikes on three targets within Iran. He wrote: “When I asked how many will die. 150 people, sir, was the answer from a General. 10 minutes before the strike I stopped it, not proportionate to shooting down an unmanned drone.
“I am in no hurry, our Military is rebuilt, new, and ready to go, by far the best in the world. Iran can NEVER have Nuclear Weapons, not against the USA, and not against the WORLD!”
Shortly after posting the tweets, Mr Trump seemed relaxed and was pictured holding a baby at the Congressional Solstice picnic at the White House.
Congressional leaders who attended a secret briefing on the potential strikes the day before said he seemed genuinely reluctant to push the button.
“We know Trump wants to avoid conflict at all costs. Even before his tweet, there was a controlled message from the administration explaining he had stood down,” said regional analyst Kyle Orton.
“Everything we know about him suggests that he would not have made that strike. It’s an attempt to get leverage and force Tehran to the table for what he calls a better deal.”
But others said the tension between the countries will remain for the foreseeable future.
Richard Nephew, the Obama government’s sanctions expert, said: “There is a view that now both countries have had a good scare, they may broker new diplomatic relations through Oman.
“But what’s more likely is we give it a couple of weeks, until Iran resumes its uranium enrichment programme, before we see a re-escalation of rhetoric.”
Mr Nephew said all Democratic election frontrunners were pledging to re-engage the US with the JCPOA, adding: “It’s safe to say Tehran is waiting for 2020 and whether Trump wins again.”
Meanwhile, London mayor Sadiq Khan kept up his war of words with Mr Trump yesterday, labelling the US leader “a 6ft 3 child in the White House”.
Mr Trump has previously called Mr Khan a “stone cold loser” and mocked his height.