“That gives you some idea of the intensity… (it) is perhaps more than we’ve seen of recent times,” he told BBC Radio in a phone interview from aboard the frigate.
“The Iranians seem to be keen to test our resolve, test our reactions most of the time,” King added.
“They’ll claim that perhaps our presence is illegitimate, even though we’re completely lawfully in international waters.
“They may also run boats in at speed towards us, to test what warning levels we get to.”
Montrose, on a three-year deployment in the region since April based at a British naval hub opened in Bahrain last year, began the escorts through the world’s busiest oil shipping lane earlier this month.
It followed Iranian threats of retribution for Royal Marines helping Gibraltar — a British Overseas Territory — seize one of its tankers on July 4 on suspicion it was carrying oil to Syria in violation of EU sanctions.
Despite Montrose’s presence in the Gulf, Iran intercepted the British-flagged tanker “Stena Impero” on July 19 as it made its way through the strait and has detained the ship at an Iranian port.
Britain on Monday ruled out swapping the tankers, and has proposed the formation of a European-led naval escort mission for global shipping through the Strait of Hormuz.
It comes as US President Donald Trump exerts a “maximum pressure” campaign of economic sanctions and stepped-up military presence aimed at forcing Tehran to renegotiate a landmark 2015 nuclear pact he pulled out of last year.
However, amid the escalating tensions King said contact with Iran remained “professional” and “cordial” on the choppy waters of the Gulf.
“There’s a healthy understanding, shall I say a respect between mariners, which now seems to be established,” he added.
Montrose will return to port later this week for pre-planned maintenance and crew changeover, and will be replaced by HMS Duncan, a destroyer which arrived in the region on Sunday.
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© Agence France-Presse