The Government hopes to secure a deal on reforms which will see European human rights judges intervene less in British affairs.
Justice Secretary Ken Clarke is hosting a conference of representatives of the 47 member nations of the Council of Europe in Brighton. The deal, called the Brighton Declaration, is expected to be signed at the two-day conference.
It comes in the wake of the ongoing furore over Government attempts to deport terror suspect Abu Qatada and after European Court of Human Rights (ECHR) judges ruled last week that the extradition of radical cleric Abu Hamza and four other terror suspects to the US would not violate their human rights.
In January in a speech at the Council of Europe, Prime Minister David Cameron claimed that the Strasbourg-based court's work defending human freedom and dignity was being put "under threat" due to public unease over some of its decisions. He also envisaged reforms to the court - reforms which senior government officials denied had been watered down into the draft Brighton Declaration.
Also on Wednesday, in contrast to what Mr Cameron has said, a justice minister involved in the reform talks insisted there was no "great constitutional crisis about foreign judges trying to ride roughshod over British law".
Lord McNally said: "I don't believe we've got some great constitutional crisis about foreign judges trying to ride roughshod over British law or British processes."
He said the court needs to change because there is a danger of it acting as a "convenient safety net" for under-performing states. The Liberal Democrat peer said national responsibility for human rights runs through draft plans for reform "like the letters through a stick of Brighton rock".
The Brighton Declaration would ensure there was "an onus at national level" for them to consider all human rights implications, he said. The ECHR "cannot secure the rights and freedoms of 800 million people and, what is more, we should not even ask them to try", he added.
As the conference got under way, Sir Nicolas Bratza, the president of the human rights court, said "no magic wand" would emerge from the talks.
He said the conference had been "talked up too much", adding: "I don't expect the dramatic changes that some have anticipated."