The shocking 23 per cent figure is the equivalent of 370,000 of the 1.6m Muslims living in the UK.
And it is almost double previous opinion polls suggesting 13 per cent believe the atrocity, which claimed 52 innocent lives, could be justified.
It will re-ignite the debate over whether the Government and Muslim leaders are doing enough to tackle extremism.
Despite protests from the Prime Minister, it is widely accepted the wars in Afghanistan and Iraq have radicalised young Muslims in Britain.
But the fact so many believe it is a justification for mass murder will be deeply disturbing for Tony Blair.
The latest survey of 1,000 Muslims, for a Channel Four Dispatches documentary to be screened tonight, contains a series of alarming findings.
Almost four in ten believe another attack will be launched by British-born Muslim terrorists.
A third of Muslims said they so disapprove of the freedoms allowed in this country they would rather live under Sharia law.
The law, which is practised in large parts of the Middle East, specifies stonings and amputations as routine punishments. A third of Muslims said they also dream Britain will one day become an Islamic state.
Four in ten think Diana, Princess of Wales, was killed to stop her marrying a Muslim, her lover at the time of her 1997 death, Dodi al Fayed.
The survey also reveals Muslims have deep concerns about the moral fabric of the country they live in.
Some 40 per cent say Britain is a country of bad moral behaviour, while 66 per cent say British parents allow their children too much freedom. A total of 44 per cent would rather send their children to a state funded Muslim school.
Half said police stop and search too many Muslims. But 80 per cent say that someone who knew of a terrorist act and did not report it would be equally to blame as the terrorists themselves.
Inayat Bunglawala, spokesman for the Muslim Council of Britain, said some of the survey’s findings were ‘staggering’.
He added: ‘Many, many people in this country, both Muslim and non-Muslim, understand that our participation in the so-called war on terror and Iraq and Afghanistan have – far from increasing our country’s national security – have actually undermined it.
‘But there is never any justification for indiscriminate acts of terrorism that target innocent civilians. That can never be justified.’
On Sharia law, he said Muslims in Britain were fortunate enough to live in a country where they could achieve changes to the law through peaceful, democratic protests.
Mr Bunglawala added: ‘That is how it should be. I find the figure of one-third wanting Sharia law just staggering’.
Mr Blair recently condemned Muslim leaders for appearing to sympathise with extremists.
He said moderate Muslims must stand up and say they disagree with the grievances of the hardliners – not just their actions.
Mr Blair declared: ‘I am not the person to go into the Muslim community and explain to them that this extreme view is not the true face of Islam.
‘People should stand up and not merely say, ‘You are wrong (but) you are wrong in your view about the West, you are wrong in your sense of grievance, the whole ideology is profoundly wrong’.’
But Muslim leaders hit back by saying the Government’s promise to do more to achieve integration in the wake of July 7 had amounted to very little.
Very few recommendations made by the Home Office’s Muslim taskforce have been taken up. Shadow Home Secretary, David Davis, said today: ‘We need to promote better integration, and with it a reduction in Islamophobia. This will require a major effort and is not just a problem for the Muslim community, as the Government have previously hinted, but it is a collective problem.
‘Britain has a proud history of tolerance and respect towards people of different views, faiths and backgrounds. But we should not flinch from demanding the same tolerance and respect for the British way of life.’
A previous poll, for The Times newspaper, found 13 per cent of British Muslims supported the July 7 bombings. Some 16 per cent said that while the July 7 attacks – which claimed 52 innocent lives – may have been wrong, their cause was right.
Dispatches: What Muslims Want is screened on Channel 4 at 8pm tonight.