It is believed the woman has been sentenced to 10 years in jail, though her alleged offence is not yet known.
It is thought that both women are now being kept at Evin prison in Tehran, the same jail where British-Iranian mother Nazanin Zaghari-Ratcliffe has been held on spying charges since 2016.
The Foreign Office said it was clear the ship's cargo had been transferred to the Assad regime in an "unacceptable violation" of global trade sanctions.
Separately, a female blogger, who is also a dual British-Australian national, was detained along with her Australian boyfriend about 10 weeks ago, the newspaper said. The 41-year-old British-Iranian national has been incarcerated in the facility after being seized on spying charges in 2016.
Citing its "privacy obligation", the department said that it would not be releasing any additional information following the initial statement.
The Australian government updated its travel advisory for Iran on September 9 stating "due to the risk that foreigners, including Australians, could be arbitrarily detained or arrested", travelers should reconsider their need to travel to the country.
Iranian authorities are told the woman she is being held in a bid to orchestrate a prisoner swap with Australia, according to The Times.
"It is now clear that Iran has breached these assurances and that the oil has been transferred to Syria and (President Bashar al-Assad's) murderous regime", the British Foreign Office said Tuesday.
The detention of two dual British-Australian citizens, if confirmed, would deepen tensions between London and Tehran and pose a further challenge to embattled Prime Minister Boris Johnson.
"All Australian citizens and holders of dual nationality with Australia who are travelling to or through Iran are urged to follow the travel advice on the DFAT Smartraveller website".
It was unclear when or why the lecturer was arrested, the newspaper said.
The latest arrests are also raising questions over the safety of travellers from other nationalities.
It will come amid a downturn in relations in between Britain and Iran, sparked by problems together with the seizure by the Royal Marines in July of an Iranian oil tanker in the vicinity of Gibraltar.
Britain and Australia last month signed onto a US -led maritime security mission to protect worldwide shipping in the Strait of Hormuz, where Iran's recent seizures of vessels has raised tensions with the West.