BRUSSELS — When cracks recently appeared in beams of the European Parliament’s main chamber, forcing its closing, one member, Nigel Farage of the U.K. Independence Party, proclaimed that he would “work for the day that the whole democratic facade of the European Parliament is shut as well.”

Mr. Farage is an avowed anti-European known for extreme views. But even for Europeans who do not actively resent the Parliament, it has become a powerful symbol of how institutions designed to build a united Europe have faltered as the project faces the most serious crisis of its 60-year history.

A poll conducted last November found “a sharp decline” in the European Parliament’s image compared with a similar poll in 2008, when Europe’s economic crisis bloomed. The Eurobarometer, conducted by TNS, found that 26 percent of the 26,594 people sampled from across Europe had a “negative” view of the Parliament, an increase of 9 percentage points.

The Parliament’s “diminishing legitimacy and authority,” said Fredrik Erixon of the European Center for International Political Economy, a research group in Brussels, was “really very worrying at a time when people have been protesting in the streets against diktats from Europe to fix their economies.”