LONDON — Britain’s fraught relations with Europe’s top human rights court worsened Tuesday when judges there ruled that life sentences handed to three convicted murderers amounted to inhuman and degrading treatment because they had no hope of release.

The decision came just two days after the deportation of the militant Islamic cleric known as Abu Qatada to face terrorism charges in his native Jordan.

That step had been held up for years, partly because of the European Court of Human Rights, which is based in Strasbourg, over worries that evidence obtained under torture would be used against him in Jordan.

Established in 1959, the court rules on claims of violations of the European Convention on Human Rights. It is not part of the European Union’s structures, but its judgments are binding on countries that have signed the convention and have led many governments to alter specific laws to comply.