Eliza Manningham-Buller said: “We are faced with a realistic possibility of a form of unconventional attack that could include chemical, biological, radiological or nuclear (CBRN).
“It is only a matter of time before a crude version of a CBRN is launched on a western city.”
The warning came just one day after police in the former Soviet republic of Georgia said a taxi driver was detained after police found nerve gas and radioactive materials “that can make a “dirty bomb in his cab.
Tedo Mokeliya was detained after police in the capital, Tblisi, discovered two containers holding cesium-137 and strontium in his taxi.
Cesium and strontium, which have medical and industrial applications, also are considered likely ingredients for a so-called “dirty bomb”, in which conventional explosives are combined with radioactive material.
Police also found a dark brown liquid, later determined to be nerve gas concentrate.
Police said the illicit materials might have been earmarked for sale in Turkey.
Thefts of the materials became common after the 1991 collapse of the Soviet Union and, according to some estimates, dozens of such containers remain unaccounted for.
But the director-general of MI5 said intelligence suggested that “renegade scientists” had given terrorist groups the information they needed to create such weapons and that they would become more sophisticated.
But she added that conventional bombs and suicide bomb attacks remained their preferred weapons.
“They [al-Qaida] still remain an organisation capable of deadly terrorist attacks,” she said.
“The threat from international terrorism is with us for a good long time. If this is a war that can be won, it is not going to be won soon.
"The supply of potential terrorists among extreme elements is unlikely to diminish. Breaking the link between terrorism and religious ideology is difficult.”
Ms Manningham-Buller was making her first on-the-record speech since taking on her new job in October last year.
Since becoming director-general of the British home security service, she has been involved in countering the ricin plot and was involved last month in the review of vulnerable targets in London which led to a ring of concrete protection being placed around the Houses of Parliament.
Britain was put on its second highest security alert last month.
It would move to the top alert if there was specific intelligence about a time, place or target for an attack.
Ms Manningham-Buller told a conference at the Royal United Services Institute in central London that al-Qaida was “the first truly global threat.”
Recent attacks in Riyadh and Casablanca proved it and other groups still posed a “potent threat”.