Numbering up to two million in a nation of some 60 million, Muslims could be a swing force in close races, their vote highlighting the influence of global politics on local elections, pollsters say.
"Vote, and vote right" the Muslim Association of Britain (MAB) urged its members, issuing a list of preferred candidates that virtually boycotts Blair's party.
Labour has put "a stigma on the Muslim community", the association's press officer Ihtisham Hibatullah said.
"The Muslims are being looked down upon, seen as something to fear," he said, adding: "We hold the government directly responsible."
In recommendations for six key races, MAB lists only one Labour member - London's fiercely anti-war mayor, Ken Livingstone, who only recently rejoined the party.
The other favoured candidates are from the anti-war Respect party or the Greens.
Muslim groups fear that an expected turnout of only one in three may favour far-right parties on Thursday, and have urged Muslims to vote strategically.
"I have to say that on the whole it would be absolutely foolish... if the Muslims threw their vote away by giving it to Respect," said Pakistan-born Baroness Kishwer Falkner, a Muslim member of parliament's upper chamber, the House of Lords.
London mayor Ken Livingstone
has the backing of some Muslims
Falkner denounced the MAB list, calling Respect "a single-issue party (that) cannot build the critical mass".
"As Muslims, we shouldn't be interested in protesting, but in parties that can change something."
Her Liberal Democratic party, which strongly opposed the Iraq war, has most to gain from Labour's falling popularity among British Muslims, and has climbed to compete with the Conservatives as the main opposition grouping.
"Iraq is what has made (Muslims) open the door to the Liberal Democrats, and then they like what they see," Falkner said.
While Blair's party has seen its support among Muslim voters fall from 75% in the 2001 election to 38% today, Liberal Democrats now are backed by some 36% of Muslims, according to The Guardian newspaper.
Visiting a mosque last week in the Welsh capital Cardiff, Liberal Democrat leader Charles Kennedy said his party was trying to engage in "as much dialogue as they can" with Muslims.
"Muslims are made
to feel that they do
not truly belong here, they feel that they
are not truly accepted, let alone welcomed,
as full members of
Commission on British Islamophobia report
He also criticised the "terrible errors" of British foreign policy over the past two years.
The Iraq war and British domestic policies aimed at fighting extremism have shifted political debate from social and regional questions to global issues.
They have also mobilised Muslims at a time when experts warn of rising Islamophobia across Britain and a possible backlash.
"Muslims are made to feel that they do not truly belong here, they feel that they are not truly accepted, let alone welcomed, as full members of British society," a report by the Commission on British Islamophobia said last week, warning that a "time bomb" of extremism was set to go off.
Another group, the Muslim Council of Britain, urged all members of the faith to vote strategically to fight far-right parties also running on 10 June.
Muslims must vote, it said in a letter last Thursday, "in order not to let in the racist and far-right parties simply by default, which could happen if people do not vote".
"We understand that many Muslims are disillusioned," the council's media coordinator, Inayat Bunglawala, said. "They turned out in huge demonstrations (against the war) last year, and most politicians ignored them."
But he said the council gave no voting preferences, just the call to participate to oppose groups such as the far-right anti-immigration British National party, which hopes to make it past the five per cent mark to join the London Assembly.
The council wants to see "Muslim-friendly candidates" win, he said.
He was certain that Thursday's vote would go far beyond local concerns and focus on Blair's taking Britons to war. "Iraq is definitely going to be a major factor," Bunglawala said.