In a dramatic escalation of tensions, Iran's Islamic Revolutionary Guard Corps seized the Stena Impero on Friday in the strategic Strait of Hormuz.
It came two weeks after British authorities seized an Iranian tanker off Gibraltar on suspicion of breaching sanctions against Syria, and against a backdrop of brinkmanship between Washington and Tehran.
The government's emergency Cobra committee met over the weekend and May was to chair another meeting on Monday, while Foreign Secretary Jeremy Hunt is later expected to update parliament.
The EU has condemned Iran's action and Hunt spoke to his French and German counterparts on Sunday.
They agreed that "safe passage for vessels through the Strait of Hormuz is a top priority for European nations, while avoiding any possible escalation in the region", a British statement said.
Tensions in the Gulf have ramped up since May, when the US boosted its military presence in response to what it called indications of a "credible threat" from Iran.
The British government had warned its ships to avoid the Strait of Hormuz, a chokepoint for about a third of the world's sea-borne oil.
But questions are being asked in London about why it was not more proactive in protecting ships after the Gibraltar incident, which provoked fury in Tehran.
The standoff comes at a sensitive time for Britain, with May due to resign on Wednesday over her Brexit strategy, with former foreign minister Boris Johnson the overwhelming favourite to replace her.
- 'Illegal interference' -
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Junior defence minister Tobias Ellwood said Sunday that Britain would be looking "at a series of options" on how to respond to Iran's actions.
Iranian authorities said they detained Stena Impero after the tanker failed to respond to distress calls and turned off its transponder after hitting a fishing boat.
But in a letter to the UN Security Council, British charge d'affaires Jonathan Allen accused Tehran of "illegal interference".
He said there was no evidence of a collision and said the vessel had been in Omani waters with its transponder switched on when it was approached.
Iranian authorities have said the fate of the Swedish-owned tanker depends on the cooperation of its crew.
But they insisted the 18 Indians, including the captain, three Russians, a Latvian and a Filipino on board are all in good health and anchored in a safe place.
Iran released video footage showing the tanker being surrounded by speedboats before troops in balaclavas descend a rope from a helicopter onto the vessel.
In an audio recording of a radio exchange obtained by a London-based maritime firm, an Iranian officer can be heard ordering the tanker to change course "immediately".
The British frigate HMS Montrose, which was in the Gulf at the time, intervenes to inform the Stena that its passage must not be impaired under international law.
The Iranians reply: "No challenge is intended... I want to inspect the ship for security reason."
- US, Iranian brinksmanship -
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European powers have been drawn into an escalating row between the United States and Iran.
Tehran has been at loggerheads with Washington since May 2018, when President Donald Trump unilaterally withdrew the US from a landmark 2015 deal putting curbs on Iran's nuclear programme in exchange for sanctions relief.
The US administration reimposed tough sanctions on Iran, which retaliated by increasing its enrichment of uranium beyond limits set in the nuclear accord.
Since May, a number of ships have been sabotaged or attacked in the Gulf, while in June, Trump called off air strikes against Iran at the last minute after Tehran downed a US drone.
Britain summoned Iran's charge d'affaires on Saturday over the seizure of the Stena Impero.
The incident began hours after a Gibraltar court extended by 30 days the detention of the Iranian tanker, Grace 1, seized on July 4.
Amid the standoff, the UN's nuclear watchdog, the International Atomic Energy Agency, announced Monday that its longtime head Yukiya Amano had died after suffering from poor health for some time.