Mr Hague said the UK would work with EU partners to impose sanctions on those responsible to help bring an end to the violence.
The report, Torture Archipelago: Arbitrary Arrests, Torture and Enforced Disappearances in Syria's Underground Prisons since March 2011, includes maps locating detention centres, video accounts from former detainees and sketches of torture techniques.
Almost all the former detainees interviewed by Human Rights Watch said they had been subjected to torture or witnessed the torture of others during their detention.
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Levels of safety are not high enough in prisons, meaning that reform of inmates cannot take place, Prisons Minister Sam Gyimah has said.
The Government's Prevent campaign is "simply not trusted" by many British Muslims, the Independent Reviewer of Terrorism Legislation said.
The former Labour minister criticised the government's approach to leaving the European Union.