The Duncan, a type 45 destroyer, is currently in the Mediterranean on a Nato exercise and had been due to relieve the Montrose when it comes off duty for maintenance and repairs.
But its deployment has been brought forward because of heightened tensions in the Gulf. The move will ensure that the royal navy maintains continuous frigate presence in the region with the two ships set to operate alongside one another for a short period.
“As part of our long standing presence in the Gulf, HMS Duncan is deploying to the region to ensure we maintain a continuous maritime security presence while HMS Montrose comes off task for pre-planned maintenance and crew change over," the Ministry of Defence said in a statement.
"This will ensure that the UK alongside international partners can continue to support freedom of navigation for vessels transiting through this vital shipping lane."
The deployment comes amid increased tension between Iran and the west after the US withdrawal from the 2015 nuclear deal and tightening of restrictions on trade with Iran.
The UK and other world powers have sought to salvage the nuclear deal, in which Iran was to curtail its atomic programme in exchange for normalised economic relations. But Iran has complained that the Europeans are not holding up their end of the bargain by mostly abiding by the US sanctions.
Particularly painful for Iran have been restrictions placed on the sale of its oil and gas, the lifeblood of its economy. Iran has begun to downgrade its commitment to the nuclear deal and up its enrichment of uranium in response to the lack of economic benefits.
The UK, France and Germany have warned Iran that such moves could cause the deal to collapse, but Iran says it was not gaining anything from upholding the agreement and that Europeans were mostly abiding by the US restrictions.
News of the ship deployment came as Downing Street confirmed that the UK is in discussions with the US over a possible boost to their military presence in the Gulf.
A No 10 spokeswoman said: “We have had a permanent presence there for a long period of time, since the 1980s, and we have a number of military assets already in the region.
“The US has been discussing with a number of countries, including ourselves, how we might build on this. Those discussions are currently ongoing.
“We are talking to the US about building on our presence in the face of recent threats to shipping in the area.”
The UK's naval alert has been raised to its highest level in the region, with British-flagged ships notified at the beginning of the week that Iranian waters were considered a level three – or “critical” – security environment.
The move came after Iran threatened reciprocal action for the seizure of the tanker Grace I by the royal navy near Gibraltar, on suspicion of attempting to breach international sanctions on Syria.
Iran is now demanding the release of its tanker, warning of “consequences” if it is not allowed to continue on its way.
The UK tanker British Heritage was approached by three boats of the Iranian Revolutionary Guard Corps on Wednesday and ordered to stop in Iranian territorial waters.
But the HMS Montrose, which was escorting the ship, turned its guns towards the Iranian craft and ordered them away.
“The legal pretexts for the capture are not valid," Abbas Mousavi, an Iranian government spokesman, said. "The release of the tanker is in all countries' interest."
He threatened reciprocal measures against the UK if the tanker was not allowed on its way.
Asked for the UK’s response to Tehran’s demand, the No 10 spokeswoman deflected: “We are concerned about the threats that they are making to disrupt shipping in the area. We are urging them to de-escalate tensions in the region and we think that’s the best course of action for everyone.”
The foreign secretary. Jeremy Hunt, told the Daily Telegraph the British Heritage incident was “deeply troubling” and highlighted the fact that “we have run down the navy too much”.
“Our current commitment is for 19 destroyers and frigates supported by excellent offshore patrol vessels,” said Mr Hunt. “If I become prime minister, I will review this commitment as part of a wider look at our defence capability.”
Bob Sanguinetti, CEO of the UK Chamber of Shipping, said that the intervention by the Montrose illustrated "the vital importance that the royal navy continues to play in safeguarding UK commercial interests abroad".
“UK shipping sees up to 30 flagged vessels pass through the Gulf each day, while nearly 5 per cent of UK oil and 13 per cent of UK gas moves directly through the Strait of Hormuz," said Mr Sanguinetti.
"Any action to stop or impede the innocent passage of merchant shipping is wholly inacceptable, and steps must be taken to ensure the legal and safe passage of all merchant ships in the region.
“The UK Chamber of Shipping welcomes US plans for a ‘coalition of allies’ to patrol the waters off Iran and Yemen, and will support all measures and international initiatives that preserve international law and protect the lives and wellbeing of innocent seafarers."
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