Police will be trained on the importance of the Koran and Sharia law to Muslims under Government plans to tackle extremism.
Lessons in the Islamic faith and culture will become part of the formal training for recruits.
Chief constables said officers will build better relationships by understanding the communities they are policing.
This could prove crucial in rooting out extremism and preventing a terrorist attack, according to the Association of Chief Police Officers.
But critics expressed concern that the plan could foster division, rather than combat it.
It comes after the Archbishop of Canterbury, Rowan Williams, said the adoption of certain aspects of Sharia law in the UK “seems unavoidable”.
He later said his remarks had been misinterpreted.
Shadow Home Secretary David Davis added: “Of course it is sensible for the police to have an understanding of the Koran and Sharia law as long as we do not allow the situation to slip so that Sharia law is regarded on an equal basis with British law.
“British law is and always must be pre-eminent.”
The scheme is part of a wide-ranging strategy to prevent extremist ideas gaining hold in schools, colleges and prisons.
Other initiatives in the 40-page strategy include guidance to parents on how to stop children searching for extremist websites, and intervening where convicted terrorists are suspected of spreading hate in prison.
Police will not have to learn the “depth and complexity” of Sharia law but would be expected to understand Islamic culture.
But critics have described the plan as “politically correct thinking”.
Philip Davies, Conservative MP for Shipley, said: “Police officers are not there to implement sharia law. They are there to implement British law.
“This idea is misguided. We will only get community cohesion when everybody signs up to being British and following British law.”
The so-called Prevent strategy says: “Research last year revealed that the police service would be very low on the list of agencies that the Muslim community would turn to if they had concerns about a member of their community who embraced violent extremism.
“The police service has a long way to go in building a relationship of trust around these issues.”
The Chief Constable in charge of the strategy, West Yorkshire’s Norman Bettison, said: “We work closely with communities and the majority of police training at the moment in this area is done in partnership with Muslim organisations.
“We are building on this basis of training and emphasising that a basic principle of policing is that officers work with and should understand the communities they are policing.
“The Acpo Prevent strategy recognises this in the context of non-Muslim officers working with Muslim communities.
“These issues can be complex and include nationality, community and religious issues, all of which are interwoven.
“That is what we are trying to get across to officers in our training. The depth and complexity of sharia law is not part of this training.
“The strategy remains in draft form at present and I expect it to be formally adopted by chief officer colleagues after further feedback from partners and communities.”