Communities Secretary Eric Pickles has been put in charge of turning around 120,000 problem families in the wake of the riots.
A unit headed by victims' commissioner Louise Casey will be set up in his department after wrangling over whether Iain Duncan Smith or Michael Gove at Education should take control instead.
Liberal Democrats argued that it should be placed with Mr Pickles's department because councils, where the party is traditionally well represented, have the "most levers to pull".
A Lib-Dem source dismissed as "ridiculous" suggestions they had fought to keep it away from Work and Pensions Secretary Mr Duncan Smith because of his social conservative values.
But another Whitehall insider said figures in the party were concerned Mr Duncan Smith, who set up the Centre for Social Justice think tank in opposition, was trying to "grab all the social justice agenda".
Officials in all three Cabinet ministers' departments are understood to have been keen to take on the unit, seeing it as a chance to impress the Prime Minister.
After the riots David Cameron announced plans to transform the lives of 120,000 problem families by 2015.
