The world's fifth-biggest economy could lose preferential access to its largest export market overnight, affecting every sector, leading to rising costs and disruption at British ports.
May's government then survived a confidence vote on Wednesday and set about talks with figures from rival parties.
But the main opposition leader Jeremy Corbyn stayed away, saying a "no-deal" departure must be ruled out first -- something May says is impossible.
May spoke to Dutch Prime Minister Mark Rutte and German Chancellor Angela Merkel on Thursday, and to EU leaders Jean-Claude Juncker and Donald Tusk by telephone Friday to discuss where to go next on Brexit.
EU chiefs have so far ruled out renegotiating the agreement, but have signalled they could postpone the withdrawal if May changes her "red lines" on leaving the EU's customs union and blocking free movement of citizens.