The action prompted a late night meeting of the COBRA emergency security committee chaired by Prime Minister Theresa May.
Following the meeting, security officials have warned UK shipping to stay clear of the Strait of Hormuz 'for an interim period'.
And in the early hours, the acting US Secretary of Defense Richard Spencer announced he is sending several hundred troops, as well as a glut of aircraft and air defense missiles, to Saudi Arabia in order to counter Iran’s threat.
The Royal Navy has the Type 23, frigate HMS Montrose in the region, which will be soon joined by the Type 45 destroyer, HMS Duncan.
Foreign Secretary Jeremy Hunt, who attended the emergency meeting held in the Cabinet Office Briefing Room, branded the seizing of two British oil tankers by Iran as 'completely unacceptable'. The first vessel, the Stena Impero, was surrounded by heavily-armed Iranian vessels and a helicopter around 4pm yesterday and ordered to turn north.
The second vessel, the Mesdar, is Liberian flagged, but owned by British company Norbulk Shipping, was ordered by Iran to turn north around 45 minutes later. It was later released after being boarded and inspected by Iranian troops.
The Stena Impero oil tanker has been seized by Iranian authorities while passing through the Strait of Hormuz yesterday
The Stena Impero was surrounded by Iranian Revolutionary Guard forces at 4pm and ordered to head north. The British registered vessel switched off its maritime tracker a short time later. A second British vessel, Medsar, abruptly changed course towards Iran around 4.45pm. Theresa May is expected to hold an emergency Cobra meeting this evening in response to the seizures. Today's action follows attacks on six oil tankers in the Gulf of Oman and an earlier attempt to seize a British oil tanker which was thwarted by the Royal Navy
The Iranian Revolutionary Guard uses a large number of high-speed small vessels to harass shipping in the Strait of Hormuz. The regime launched these 'ultra-fast' boats in 2010
'We remain in close contact with our international partners and there will be further meetings over the weekend.'
A spokesman for the owner of the Stena Impero said the vessel was in 'full compliance with all navigation and international regulations', when it was seized.
There are no reported injuries to the vessel's crew, who are Indian, Russian, Latvian and Filipino in nationality.
According to the company, the vessel, which was built in 2018 'is no longer under the control of the crew and remains uncontactable'.
Mr Hunt said: 'I will shortly attend a COBR meeting to review what we know and what we can do to swiftly secure the release of the two vessels - a British-flagged vessel and a Liberian-flagged vessel.
'Their crews comprise a range of nationalities, but we understand there are no British citizens on board either ship.
'Our ambassador in Tehran is in contact with the Iranian Ministry of Foreign Affairs to resolve the situation and we are working closely with international partners.
'These seizures are unacceptable. It is essential that freedom of navigation is maintained and that all ships can move safely and freely in the region.'
Iranian authorities have yet to comment on the Mesdar, but marine tracking data showed it turning dramatically off course and towards the Iranian coast.
US President Donald Trump said America would be 'working with the UK'.
He told reporters on the South Lawn of the White House as he was about to board Marine One: 'We will talk to the UK and we have no written agreement but we have an agreement. They've been a very great ally of ours.
'So we heard about it, we heard it was one, we heard it was two, and we will be working with the UK.'
He described Iran as 'nothing but trouble', but predicted the standoff would eventually work out 'very nicely'.
The president said: 'Iran is showing their colours' and said Tehran 'is in big trouble right now' because of the impact of sanctions on its economy.
Labour deputy leader Tom Watson urged caution in a series of tweets: 'These reports are a matter of real concern. We know that some days ago there was an attempt to steer a British tanker towards Iranian waters.
'Our ships have the right of safe passage and the Stena Impero must be allowed to continue its voyage unimpeded.
'Any move to seize a British tanker would be a significant and harmful escalation of a situation where de-escalation is needed.'
Foreign Secretary Jeremy Hunt, pictured on Wednesday, attended a meeting of the Cabinet COBR committee to discuss the worsening Iranian crisis
Transport secretary Chris Grayling was smiling as he left the emergency COBRA meeting in Whitehall last night
US President Donald Trump, pictured, said he was going to talk to UK authorities about yesterday's action by Iran
The vessel had left Fujairah in Dubai and moved into the Strait of Hormuz when it was intercepted.
According to Iranian state TV, the Stena Impero tanker 'was confiscated by the Revolutionary Guards at the request of Hormozgan Ports and Maritime Organisation when passing through the strait of Hormuz, for failing to respect international maritime rules.'
It is understood the British-flagged tanker was surrounded by small craft and helicopters and ordered to turn north into Iranian waters.
According to The Times, HMS Montrose, which is patrolling the Persian Gulf raced towards the scene after the British-flagged tanker diverted from its planned course.
A military source said the warship arrived ten minutes too late, by which time the tanker had crossed into Iranian waters. It is claimed the Iranians were ready to 'engage' the Type 23 frigate .
A statement from Stena Bulk, the company which owns the tanker, said the firm had lost contact with the crew of 23 after it was approached by 'unidentified small crafts and a helicopter' at around 4pm.
This image, released from Iranian state TV shows Revolutionary Guard speedboats harrying a Panamanian oil tanker on July 14
Royal Marine Commandos intercepted the Grace I off the coast of Gibraltar, on July 14. The vessel, which is Iranian owned is suspected of smuggling oil to Syria in breach of EU sanctions
A second UK-owned vessel, the Mesdar, turned dramatically towards Iran around 45 minutes after the Stena Impero was seized
According to Marine Traffic, the Mesdar turned dramatically north shortly before 5pm UK time yesterday
The statement said: 'Stena Bulk and Northern Marine Management can confirm that at approximately 1600 BST on 19th July UK registered vessel Stena Impero (built 2018, 49,683 DWT) was approached by unidentified small crafts and a helicopter during transit of the Strait of Hormuz while the vessel was in international waters.
'We are presently unable to contact the vessel which is now heading north towards Iran.
'There are 23 seafarers aboard. There have been no reported injuries and their safety is of primary concern to both owners and managers.
'The priority of both vessel owner Stena Bulk and ship manager Northern Marine Management is the safety and welfare of the crew.'
According to Norbulk Shipping UK, the crew of the Liberian-registered Mesdar tanker which was seized are 'safe and well'.
The company said the vessel was boarded by armed guards but has now been allowed to continue with its voyage.