The silver medallists are the first British quartet to step on a world championship podium since 1939.
David de Gea has enjoyed a consistent season under Erik ten Hag, and the goalkeeper is hopeful of extending his stay with Manchester United.
Resurgent Scotland are next up for Wales in Edinburgh.
Thibault Flament, Thomas Ramos and Matthieu Jalibert also got on the scoresheet in Rome for the Grand Slam champions.