LONDON — Just three days after their formal parting, Britain and the European Union were already at loggerheads Monday over a future trade deal, setting the stage for months of bluster and bickering over how to refashion their economic and political ties.

With Britain’s formal exit from the bloc on Friday night, many Britons had hoped to finally put the Brexit nightmare behind them.

But judging by the statements from both sides of the English Channel on Monday, that hope seems likely to be unfulfilled.

In remarks in Brussels, Europe’s chief negotiator, Michel Barnier, adopted a steely tone, insisting that Britain must commit to preventing unfair competition if it wants access to the market of 450 million Europeans without tariffs and quotas.