The terrorists are said to have produced the bomb using radioactive uranium that they took from Iraq’s Mosul University after capturing the city in June, the Daily Mirror reported.
The report says that the militants also sent threatening messages on social media, bragging about the destruction the bomb would cause if it went off in London.
British explosives expert, Hamayun Tariq, who left his home in Dudley, West Midlands, to join the ISIL in 2012, now training fellow Brits in Syria, was among the extremists making online threats.
The 37-year-old said in a message posted online that the ISIL "does have a dirty bomb,” adding, "We’ll find out what dirty bombs are and what they do. We’ll also discuss what might happen if one actually went off in a public area.”
He added the bomb would be "terribly destructive” if set off in London because it would be "more of a disruptive than a destructive weapon,” a claim also echoed by other ISIL militants.
Iraq's ambassador to the UN, Mohamed Ali Alhakim, said in a July letter to UN Secretary-General Ban Ki-moon that terrorist groups had seized some 40 kilograms of uranium compounds from Mosul University.
The terrorists used chemical weapons in their attacks in Syria in August 2013. However, the militants, along with the foreign-backed Syrian opposition, accused the Syrian army of being behind the deadly attack, an allegation that Damascus strongly denied.
The ISIL terrorists currently control swaths of territory across Iraq and neighboring Syria where they have been committing heinous crimes.