Iran has imposed restrictions on ships using the strait, first in retaliation for the US-Israeli bombardment of the country, and then in response to a US blockade of Iranian ports.
A Liberia-flagged container ship suffered damage to its bridge on Wednesday after being hit by gunfire and rocket-propelled grenades northeast of Oman.
The UKMTO said the master of the vessel reported being approached by an IRGC gunboat.
The vessel, it said, was subsequently fired upon.
All crew members were safe and there was no fire or environmental impact due to the incident.
Maritime security sources said three people were aboard that gunboat.
The master of the Greek-operated container ship also reported that no radio contact was made before the incident and that the vessel had been initially informed that it had permission to transit the Strait of Hormuz.
The UKMTO later said that a second container vessel had been fired upon about west of Iran.
The Panama-flagged vessel was not damaged and its crew members are safe.
Maritime security sources said a third container ship was fired upon about west of Iran while transiting outbound of the Strait of Hormuz.
The Liberia-flagged vessel, which was not damaged had stopped in the water.
Its crew was safe, the sources said.
Before the war began on February 28, the waterway typically handled roughly one-fifth of the world's oil and liquefied natural gas supply.
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