One of the main obligations of states under the third pillar of the UN Guiding Principles on Business and Human Rights (UNGPs) is to identify and remove barriers to access to judicial remedies. Among these barriers, one concerns the competence of domestic courts to exercise jurisdiction over corporate defendants in civil claims for remedy, especially over foreign-incorporated subsidiaries of transnational corporations. Both the European Parliament and the Council of Europe (CoE) have discussed whether to recommend the adoption of particular grounds for jurisdiction to their respective Member States. This contribution examines the European rules on attribution of civil jurisdiction, relevant to the type of business and human rights cases that are now ongoing in European Courts. It discusses both the regime of the Brussels-I Regulation and some particular residual grounds for jurisdiction in EU Member States recommended by the CoE and the European Parliament, and aims to assess to what extent these recommendations contribute to improving access to court in Member States.