LONDON—President Donald Trump warned U.K. Prime Minister Theresa May that a plan her government released Thursday outlining its future economic relationship with the European Union, if implemented, could “kill” the nation’s chances of striking a bilateral trade deal with the U.S.

The public rebuke of Mrs. May, published hours after Mr. Trump arrived in the U.K., marks a fresh blow to the British leader, already taking heavy fire over her approach to exiting the EU bloc in March 2019.

“If...