Yes, Barcelona is English friendly.
Many of the city's residents speak English, and you'll find that most signs and menus are also in English. This makes it easy to get around and enjoy your holiday, even if you don't speak any Spanish.
It's still worth learning a few basic phrases before you travel, though. Knowing how to say please and thank you in Spanish will go a long way, and it's also useful to be able to ask for directions.