The call comes in the wake of recent revelations that the Metropolitan Police are now investigating MI6 as well as MI5 over allegations of involvement in torture.
Citing evidence that Tony Blair and others may have been aware of policy guidance on the issue, the Liberal Democrat conference passed a motion calling for a full and independent public inquiry into the involvement or knowledge of the British Government on "matters relating to torture and extraordinary rendition".
The party says that the Government should provide the inquiry with full details on each and every policy it has adopted over the last 20 years as to how British officials should act in circumstances that may cause them to be put in danger of being complicit in torture.
It is also calling for the immediate release of the summary of the 42 intelligence documents relating to the treatment of Binyam Mohammed.
The motion also said that Tony Blair should not be supported by any British or EU Government for the post of President of the European Council before an inquiry has established his role in the formulation of British policy on torture
The Liberal Democrats also want the Government to renegotiate the terms of its agreement with the United States over the use of Diego Garcia.
The Liberal Democrat Shadow Foreign Secretary, Ed Davey said: “With the police now investigating claims of complicity in torture against both MI5 and MI6, the Government can no longer resist calls for a full judicial inquiry.
“Gordon Brown and David Miliband must come clean about what they knew and when. They must not be allowed to continue to hide behind ongoing police investigations.
“No Government can in good conscience support Tony Blair as a potential President of the European Council while it remains unclear what his role was in the development of British policy on involvement in torture.”