LONDON—Instead of closing in on a future trade deal, the European Union and Britain entered a bitter fight Thursday over a planned British law that the EU says would constitute a serious violation of the Brexit divorce agreement and destroy what little trust remains between the two sides.

EU chief negotiator Michel Barnier, center, is surrounded by delegates and pro-EU protesters as he arrives at the Westminster Conference Center in London, on Sept. 9, 2020. Alberto Pezzali/ AP Photo