Video report by ITV News Correspondent John Ray
Foreign Secretary Jeremy Hunt said there will be a European-led maritime mission focused on protecting shipping in the Strait of Hormuz.
In a Commons statement, Mr Hunt described the seizure by Iran of a British-flagged tanker on Friday as an act of "state piracy".
He also told MPs that the shipping transport security has been raised to level three.
His comments come just hours after Iran's state television agency released footage from on board the tanker which was seized by Tehran in the Strait of Hormuz.
In the images - distributed by the Fars News Agency - members of the 23-strong crew can be seen talking around a table and working in the tanker's control room and kitchen.
The footage emerged as Theresa May chaired a meeting of the Government’s emergency committee Cobra.
The Prime Minister is expected to receive updates from ministers and officials on the situation and will discuss the maintenance of the security of shipping in the region.
Mr Hunt told MPs the UK is assembling "European-led maritime protection mission" for ships in Strait of Hormuz.
"We will seek to put together a European-led maritime protection mission to support safe passage of crew and cargo in this vital region," he said.
He added: "It is with a heavy heart that we are announcing this increased international presence in the Gulf because the focus of our diplomacy has been on de-escalating tensions in the hope that such changes would not be necessary."
The Foreign Secretary continued: "If Iran continues on this dangerous path, they must accept the price will be a larger Western military presence in the waters along their coastline, not because we wish to increase tensions but simply because freedom of navigation is a principle which Britain and its allies will always defend."
Chancellor Philip Hammond insisted the Government had been “very much engaged with both the Americans and our European partners in the response to Iran’s increasing defiance of the JCPOA over the last few months”.
ITV News Correspondent Emma Murphy on the latest from Iran
A new audio recording had been released between the Iranian Revolutionary Guard and the HMS Montrose moments before the British-flagged Stena Impero was seized in the Strait of Hormuz.
In the radio recording, released by British maritime security firm, Dryad Global, an Iranian vessel tells HMS Montrose it wants to inspect the oil tanker for security reasons.
The Iranian Revolutionary Guard can be heard saying: "If you obey, you will be safe.
"Alter your course to 360 degrees immediately, over."
The recording then cuts to a message between HMS Montrose and Stena Impero, saying: "This is British warship F236.
"I reiterate that as you are conducting transit passage in a recognised international strait, under international law, your passage must not be impaired, impeded, obstructed or hampered.
"Please confirm you are conducting you are conducting transit passage in a recognised international strait."
The frigate then asks the Iranian vessel if it can confirm it is not "intending to violate international law" by attempting to board Stena Impero.
But the tanker was boarded and seized by the Iranian Revoluntionary Guard on Friday.
In a dramatic video released by the Revolutionary Guard, several small Guard boats can be seen surrounding the larger tanker as it moves through the strait.
Above, a military helicopter hovers and then several men wearing black balaclavas begin to rappel onto the ship.
The high-quality video was shot with at least two cameras, one from a speed boat-like vessel and one from the helicopter, which captured the men as they prepare to slide down a rope onto the tanker.
Despite the Stena Impero having a British flag, none of the crew were British and it was not owned by a British company.
The crew are from India, Latvia, the Philippines and Russia.
Stena Bulk, the owners of Stena Impero said they had requested permission to visit the 23 crew members who were on board the oil tanker when it was seized.
The vessel is now being held at the Port of Bandar Abbas.
In a statement, the company's President and Chief Executive, Erik Hanell, said: “I can confirm a formal request for permission to visit the 23 crew members of the Stena Impero has been made to the authorities at the Port of Bandar Abbas.
“The request has been acknowledged, but we await a formal response.
In the meantime, we will continue to co-operate and liaise with all appropriate authorities.
“All of Stena Bulk and Northern Marine Management’s efforts and focus continue to be on the welfare and safe return of our crew and supporting their families during this very difficult time.
“Our local staff in India, Latvia, Philippines and Russia are in constant touch with the families and we will continue to do everything humanly possible to keep them informed and to support them in every way we can.”
A spokesman for Iran’s Guardian Council was quoted as saying “the rule of reciprocal action is well known in international law” and that Tehran made the right decision in the face of an “illegitimate economic war and seizure of oil tankers”.
The explanation, which contrasts with a suggestion on Friday night that the Stena Impero was “violating international maritime rules” and had collided with a fishing boat, came as the UK Government warned British ships to stay away from the Strait of Hormuz.
HMS Montrose, which is patrolling the Persian Gulf to protect shipping, and earlier this month intercepted Iranian patrol boats surrounding another UK-flagged tanker, reportedly arrived minutes too late to prevent the latest incident.