Ahmed Sami Khider and Hisham Fadlallah are said to have died at the weekend.
Khider, a former student at Wallington County Grammar School in south London, had been working in Mosul and was reportedly hit by gunfire while travelling in a convoy trying to leave the city, the BBC reports.
He was one of nine students – seven of them British – from a university in Sudan to flee the country and join Islamic State fighters in Syria after graduating in mid-2014.
His parents – including his doctor father – have travelled to Khartoum, Sudan, for “a period of mourning”, the broadcaster said.
The circumstances of the death of Fadlallah, from Nottinghamshire, were unclear.
Khider had starred wearing a doctor’s stethoscope in an ISIS film urging other Brit doctors to travel to Syria and Iraq to fight the West soon after he arrived in the region.
Sitting in front of a large desk, the doctor was clean shaven and spoke in flawless English about the different medical facilities in Syria.
“I send greetings from the Islamic State, to all my dear brothers and sisters within the Islamic State and outside.
“There is actually a really good medical service being provided here. Lots of hospitals, lots of services provided.”
He warned recruits: “the caravan is leaving and I hope I will see you all here, all the doctors helping out.”
A friend told the BBC that Khider was popular and influential at university.
“All of the boys in particular looked up to him,” he said.
“They all listened to what he said and took it to heart.
“Everyone loved him. He became a leader.”