Removing the intent
Until about 5.35pm on 7 June 1981, Saddam Hussein had the ideal equipment for producing a nuclear weapon: a plutonium-producing research reactor bought in the 1970s from France. But "Osiraq", as it was called, was destroyed by Israeli jets, whose pilots were told by their chief of staff that "the alternative [to destroying it] is our destruction". The bombing run that evening destroyed the plant in just over a minute, striking before the nuclear core had been installed.
Without plutonium, it is difficult to make a modern nuclear weapon. The JIC's dossier describes on page 24 a brief "recipe" that offers plutonium (from reprocessed reactor fuel) or highly enriched uranium (HEU), that must be produced in centrifuges that separate it from less reactive uranium.
Without nuclear power plants, President Saddam has been pursuing the HEU centrifuge route. Iraq's military scientists undoubtedly have the knowledge to make an atomic weapon; that has been widely available (even from the internet) for more than a decade. The problem is putting together the elements to make a working bomb.
A working atomic weapon requires explosives to force together the fissile material into a tiny space within a few microseconds; otherwise the energy is dissipated, producing a "dirty bomb", which spreads radiation through a conventional explosion but does not give the atomic yield. The first atomic bombs were HEU weapons; they are extremely difficult to make safely (far harder than plutonium weapons) but the technology is better understood.
With no nuclear programme, "Iraq ... has no legitimate reason to acquire uranium", the dossier notes. Despite President Saddam's efforts to acquire it, sanctions appear to be effective. Even so, the dossier comments "if Iraq obtains fissile material and other essential components ... the timeline for production of a nuclear weapon would be shortened and Iraq could produce a nuclear weapon in between one and two years."
The estimate puts a great deal of faith in the expertise of Iraqi scientists; but it is probably well-placed. However, assembling the parts required to create such a weapon has apparently proved harder than the creation would be. Iraq has been seeking the pieces since 1998, and probably earlier.
The biggest problem with this threat is that the knowledge needed to create the bomb will not go away. Only removing the intent to build it will do that.