LONDON — Britain’s top judges vowed Monday to consider with impartiality the contentious question of who has the power to trigger the U.K.’s exit from the European Union — the government or Parliament.

The Supreme Court justices acknowledged that the case has aroused strong feelings over how and whether to leave the EU. It also has major constitutional implications for the balance of power between the legislature and the executive.

The court’s most senior justice, David Neuberger, opened a four-day hearing by condemning the “threats of serious violence and unpleasant abuse” directed at lead claimant Gina Miller and others arguing that Parliament should have a say.