Al-Qaida's second-in-command, Ayman al-Zawahiri, also appeared on the video on Thursday, promising similar attacks in the future.
London bomber Muhammad Sadiq Khan, a 30-year-old British national from West Yorkshire, said responsibility for the attacks on European and US cities fell squarely on the shoulders of the West.
He explained the West was backing governments that were carrying out crimes against humanity.
"Your [the West's] democratically elected governments continue to perpetuate atrocities against my people all over the world.
"Your support for them makes you directly responsible ... until we feel security, you will be our targets. Until you stop the bombing, gassing, imprisonment and torture of my people, we will not stop."
In four bombings on the London transport system on 7 July, 56 people were killed. London police believe Khan was the leader of the suicide bombers.
Slap for Blair
Al-Zawahiri also spoke at some length on the reasons for the London attacks, and described them as "a slap to the policy of British Prime Minister Tony Blair".
"And just as Blair makes light of the blood of our brothers in Chechnya, Iraq, Palestine and Afghanistan, so he also makes light of your blood too when he drew you into this war in Iraq."
The al-Qaida deputy characterised the blasts as a response to UK foreign policy "just as 9/11 was a response to America's".
Al-Zawahiri vowed 'more attacks
in enemy territory in near future'
Further, al-Zawahiri promised similar operations in "enemy territory" in the near future, particularly Europe - because it had ignored an offer of truce from al-Qaida's leader, Osama bin Ladin.
The deputy commander also directly addressed Muslim scholars in the West who condemned al-Qaida's attacks, asking them why they did not protest so loudly when "a million people starved in Iraq and when warplanes dropped bombs on innocent communities in Afghanistan ... and when Crusader forces bombed women and children in Falluja?"
Neither the British Metropolitan police force, not London's Foreign Office were prepared to comment on the video, though both said they were aware it had been broadcast.
Khan, along with two other young British Muslims of Pakistani origin and a fourth Jamaican-born Briton, blew themselves up on three underground trains and a bus in London on 7 July.
Khan visited Pakistan along with another of the bombers last year, where religious schools have been under scrutiny after some were accused of breeding extremism.
Pakistani security forces have also been searching for members of al-Qaida in remote areas of the country recently.
London's police chief Ian Blair said the bombings bore all the hallmarks of an al-Qaida operation as it was a multiple coordinated attack on a city's transport system.
Previous al-Qaida message
Last December, in a similar broadcast made by Aljazeera, bin Ladin called for a boycott of Iraq's elections and endorsed Abu Musab al-Zarqawi as his deputy in the country.
The audio message condemned the 30 January elections to elect a national assembly that drafted the new constitution.
"In the balance of Islam, this constitution is infidel and therefore everyone who participates in this election will be considered an infidel," he said.
"Beware of henchmen who speak in the name of Islamic parties and groups who urge people to participate" in the election.
He also described al-Zarqawi as the "amir" of al-Qaida in Iraq and called upon Muslims there "to listen to him".
Bin Ladin had added that his al-Zarqawi announcement was "a great step on the path of unifying all the mujahidin in establishing the state of righteousness and ending the state of injustice".