HMS Duncan has joined frigate HMS Montrose to escort vessels sailing under the British flag through the Strait of Hormuz.
HMS Montrose has so far accompanied 35 vessels through the strait, according to the Ministry of Defence (MoD).
Defence Secretary Ben Wallace said the UK continued to push for a diplomatic resolution to the situation.
He said: “Freedom of navigation in the Strait of Hormuz is vital not just to the UK, but also our international partners and allies.
“Merchant ships must be free to travel lawfully and trade safely, anywhere in the world.”
Mr Wallace added the Royal Navy will continue to provide a safeguard for UK vessels “until this is the reality”.
HMS Duncan is a Type 45 Destroyer which the Royal Navy describes as “among the most advanced warships ever built”.
Why have tensions escalated?
In response, Tehran threatened to capture a British oil tanker.
A second British-linked tanker, the MV Mesdar, was also boarded by armed guards but was released.
Tehran said the Stena Impero was “violating international maritime rules”.
HMS Montrose was alerted but it was too far away to stop the seizure.
Iran’s state-run IRNA news agency said the tanker was captured after it collided with a fishing boat and failed to respond to calls from the smaller craft.
But the then foreign secretary Jeremy Hunt said it was seized in Omani waters in “clear contravention of international law” and then forced to sail into Iran.
The tanker’s Swedish owners, Stena Bulk, said it had been complying with regulations and had been in international waters.
Stena Bulk said the 23 crew members, who are Indian, Russian, Latvian and Filipino, are in good health and have met with officials from their respective countries.
How has the UK reacted?
But he insisted: “Our priority continues to be to find a way to de-escalate the situation.”
Speaking to the BBC, former Cabinet minister Iain Duncan Smith described the UK-flagged ship’s capture as a “major failure” by the UK.
The then defence minister Tobias Ellwood told Sky News “it is impossible simply to escort each individual vessel”.
What has Iran said?
He said Iran guarantees the security of the Gulf and the Strait of Hormuz, and insisted its action were to “uphold international maritime rules”.
Iranian President Hassan Rouhani has indicated the Stena Imepero could be released if the UK returns the Grace 1.
In a statement on his website he said: “We are not going to continue tensions with some European countries and if they are committed to international frameworks and abandon some actions, including what they did in Gibraltar, they will receive a proper response from Iran”.