Bradley Cooper -- Taking Irina Shayk for a Ride

You know Bradley Cooper's getting serious when he parades a lady friend around town, instead of hiding her from photogs -- and supermodel Irina Shayk is now firmly in that category after a night out in London.

The really, REALLY good-looking pair were all smiles Monday night, and after hanging with friends ... they climbed into a cab together ... still giddy.

BTW, Bradley and the Russian top model were hanging at Novikov Restaurant, known for its Wagyu tacos, Hamachi carpaccio and generally drawing smoking hot customers in skimpy dresses.