In the recording, what is thought to be an Iranian vessel can be heard telling HMS Montrose, it wants to inspect the tanker for security reasons, reported the BBC.
The Stena Impero was boarded by Iranian authorities on Friday. The tanker has 23 crew members of Indian, Russian, Latvian and Filipino nationalities aboard.
The Foreign Secretary has urged Iran to reverse the tanker's "illegal" seizure.
In the radio recording, which was obtained by the British maritime security firm Dryad Global, the Iranian vessel can be heard telling a ship - thought to be the Stena Impero - to change its course, saying: "If you obey you will be safe."
HMS Montrose then identifies itself and tells the Stena Impero: "As you are conducting transit passage in a recognised international strait, under international law your passage must not be impaired, impeded, obstructed or hampered."
The frigate then asks the Iranian vessel to confirm it is not "intending to violate international law" by attempting to board the tanker.
The Stena Impero was seized by the Iranian Revolutionary Guard on Friday in a key shipping route in the Gulf. Tehran said the vessel was "violating international maritime rules".
Footage emerged on Saturday appearing to show the moment the tanker was raided. It was released by Iran's Revolutionary Guard-affiliated Fars news agency.
It shows masked forces dropping down ropes on to the ship from a helicopter after it was surrounded by high-speed vessels.
HMS Montrose was alerted and raced to intervene, as it did - successfully - with another British-flagged tanker just over a week ago.
But this time it was too far away to stop the Stena Impero being seized - the tanker was already in Iranian waters.
Iran's 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 Hunt said it was seized in Omani waters in "clear contravention of international law" and then forced to sail into Iran.
The Stena Impero's Swedish owners, Stena Bulk, said it had been fully complying with regulations and had been in international waters at the time.
It said the crew members were in good health.
A second British-owned Liberian-flagged tanker, the MV Mesdar, was also boarded by armed guards on the same day but was released.
It came after Royal Marines helped seize Iranian tanker Grace 1 off Gibraltar earlier this month, because of evidence it was carrying oil to Syria in breach of EU sanctions.
Iran described the incident as "piracy" but Hunt said the Grace 1 was detained legally in Gibraltarian waters "totally within the law".
( With inputs from IANS )