Reports say that 32-year-old British-born father Kabir Ahmed, from Derby was travelling in a truck packed full of explosives which drove into a police convoy and detonated in the northern Iraqi city of Baiji.
Eight people were killed in the incident, while a further 15 were injured.
There has been no British confirmation that Ahmed was part of the attack, despite IS militants naming him as one of the people involved.
The Foreign Office said it was aware of the death of a British national in Iraq, but could not confirm whether it was part of the suicide attack.
Shiraz Maher, from the International Centre for the Study of Radicalisation at King's College in London, who monitors the actions of British jihadists overseas, said that Ahmed, who also goes by the name of Abu Sumayyah, was involved in the incident.
He wrote on Twitter: "British foreign fighter, Abu Sumayyah, (real name: Kabir Ahmed) from Derby carried out a suicide bombing in Baiji, Iraq, yesterday.
Maher added that the 32-year-old "originally joined Jund al-Sham in Syria and then moved to Islamic State."
Ahmed was one of the first people in Britain to be convicted of spreading hate campaigns about homosexual people.
He was part of a group who handed out pamphlets saying homosexuals deserved to be executed.