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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Labour strongholds tended to remain so - apart from a major loss for the party in Dudley.
Labour suffered a "terrible" defeat in Rhondda but has already won 16 Welsh Assembly seats as it looks to record a fifth term in office.
UKIP have made further gains in the local elections in the Anglia region and the Conservatives have won back control in Peterborough.