Defence Secretary Philip Hammond plans to investigate claims by 180 Iraqis that they were tortured by British soldiers through the Iraq Historic Allegations Team (IHAT), which includes members of the Royal Navy Police (RNP).
But the Public Interest Lawyers representing the Iraqis argue justice requires a fully independent public inquiry. Ministry of Defence lawyers are opposing the application.
An MOD spokesman recently said: "The IHAT is the most effective way of investigating these unproven allegations rather than a costly public inquiry."
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The PM promises to double to 200,000 the number of homes built under an existing scheme aimed at easing Britain's housing shortage.
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The plan, which would effectively strip banks of the benefit of recent corporation tax cuts, forms part of the party's election manifesto.