The videoed butchery of Fusilier Lee Rigby outside Woolwich barracks last May was a horrific act and his killers' murder conviction a foregone conclusion. Rigby was a British soldier who had taken part in multiple combat operations in Afghanistan. So the attack wasn't terrorism in the normal sense of an indiscriminate attack on civilians.

The killing of an unarmed man far from the conflict, however, by self-appointed individuals with non-violent political alternatives, isn't condoned by any significant political or religious tradition. Quite apart from morality, the impact was violently counter-productive for the Muslims that Rigby's killers claimed to be defending, as Islamophobic attacks spiked across Britain.

But the determined refusal of the political establishment to recognise the link with the wars they have been waging in the Muslim world is toxic and dangerous. Echoing the recycled nonsense of his predecessors, David Cameron claims Woolwich was "an attack on the British way of life".

The answer, he insists, is to "confront the poisonous narrative of extremism", ban the "hate clerics" - anything but mention the war. More than a decade after the launch of a campaign that has delivered mass slaughter, torture, kidnapping and destruction across the Muslim world, such deceitful inanities are simply designed to hide the political elite's role in the violence.

There can't, after all, be the slightest doubt about what Rigby's killers thought they were doing. Michael Adebolajo spelled it out on the streets and in court. This was a "military attack", he claimed, in retaliation for Britain's occupation and violence in "Muslim lands", from Iraq to Afghanistan and beyond.

"Leave our lands and you can live in peace," the London-born Muslim convert told bystanders. The message couldn't be clearer. It was the same delivered by the 2005 London bomber, Mohammed Siddique Khan, and the Iraqi 2007 Glasgow attacker, Bilal Abdullah, who declared: "I wanted the public to have a taste" of what its government of "murderers did to my people".

To say these attacks are about "foreign policy" prettifies the reality. They are the predicted consequence of an avalanche of violence unleashed by the US, Britain and others in eight direct military interventions in Arab and Muslim countries that have left hundreds of thousands of dead. Only the wilfully blind or ignorant can be shocked when there is blowback from that onslaught at home. The surprise should be that there haven't been more such atrocities.

Mainstream Islamic teaching supports the right to resist foreign occupation, while rejecting violence against non-combatants or outside the battlefield. But it is the US and its closest allies in the war on terror who have declared the whole world to be a battlefield, in which they claim the right to kill whoever they deem to be a threat.

British and US special forces have been doing that in Somalia. The US routinely kills large numbers of civilians in drone strikes across the Muslim world – 12 were reported incinerated last week in Yemen. By waging a war without borders, often against unarmed or unidentified victims, they have fatally blurred the boundaries and invited their enemies to do the same. That was Adebolajo's view of the Woolwich attack, his brother Jeremiah told al-Jazeera TV: "The geographical location of the battlefield, since this war on terror, has basically disappeared."

What is clear is that denying the role of US-British wars and killing in fuelling domestic terror attacks can only inflame Islamophobia – and absolve politicians from their responsibility for years of bloodshed and backlash. Unless the pressure grows to halt the terror war abroad, Woolwich certainly won't be the end of it at home.