* Muslims express shock at murder at start of Eid festival
* Prime Minister Cameron says Henning was simply trying to help
* Cameron vows to use all Britain's assets to fight insurgents (Adds family statement)
By Stephen Addison
LONDON, Oct 4 (Reuters) - Muslim groups across Britain united on Saturday to join Prime Minister David Cameron in condemning the beheading of aid worker Alan Henning by Islamic State insurgents.
Prayers for the 47-year-old taxi driver were said in mosques throughout Britain at the start of the Muslim Eid al-Adha festival, as his family said they were numb with grief.
Cameron called Henning a gentle, compassionate man who had simply tried to help others, and said Britain would do all it could to destroy his killers.
British media had focused on Henning as an ordinary, middle-aged non-Muslim who had given up his time and left behind a wife and two teenage children to help Muslim friends drive informal aid convoys to the victims of Syria's civil war.
"We will use all the assets we have ... to defeat this organization, which is utterly ruthless, senseless and barbaric in the way it treats people," Cameron said in a televised statement after meeting the heads of Britain's armed forces and intelligence agencies.
Henning had been held in Syria for nine months before a video was posted on YouTube on Friday showing him kneeling against a desert setting before a masked man holding a knife.
The man spoke briefly with the same southern British accent as the killer of previous hostages, widely dubbed "Jihad John."
A second video featuring an unmasked, apparently British fighter pouring scorn on Cameron for failing to send in ground troops was being urgently examined by police on Saturday, Cameron's office said.
Henning was the fourth Western hostage to be beheaded by Islamic State, which has been attacked by U.S., British, French and Arab fighter jets since seizing swathes of Iraq and Syria.
His case had prompted a wave of appeals for his release from British Muslim leaders.
Shuja Shafi, Secretary General of the Muslim Council of Britain, called his murder "a despicable and offensive act."
Imam Asim Hussain of the Manchester Central Mosque said it was a "cowardly and criminal act of appalling brutality, by a group who do not represent Islam at all."
Henning's aid convoy had been taking supplies to a hospital in northwest Syria last December when it was stopped by gunmen.
Fears for his safety had grown since the British parliament voted last month to authorize British involvement in air strikes against Islamic State in Iraq.
In the YouTube video, Henning appears to read from a script before being killed. "Because of our parliament's decision to attack the Islamic State, I, as a member of the British public, will now pay the price for that decision," he says.
Britain's Muslim leaders have in the past been accused of being reluctant to publicly confront Islamic extremism.
Henning's case prompted a united response, however.
Last month, a letter signed by over 100 British Imams and Muslim leaders said the threats to Henning had no justification in Islam. "This is not Jihad (Holy war) - it is a war against all humanity," it read.
Henning's wife Barbara and his two teenage children said they were devastated at the loss of a man who had cared about the welfare of others. "He will be remembered for this and we as a family are extremely proud of him and what he achieved," they said in a statement.
On Friday, the father of journalist John Cantlie, another Briton being held by Islamic State, appealed for his son's release.
In Brussels, the European Union's External Action Service said the EU was "committed to contribute to the fight against all terrorist groups that endanger regional and global stability," and would spare no effort to ensure that "an end is put to this atrocious terrorist campaign and all perpetrators are held accountable." (Editing by Kevin Liffey)