Flying is certainly the fastest, easiest and often the cheapest way to get to the capital of Catalonia. The flight from London to Barcelona is about two hours. Barcelona is served by three airports: Barcelona (El Prat de Llobregat), Girona and Reus. Here you can find out how to most easily get from there to the city of Barcelona.
Nevertheless cars or trains are frequently used means of transportation in order to get to Barcelona. Here you will find some good advice, as well.
If you would you like to travel from the airport to places in Catalonia, for example Blanes, Lloret de Mar, or Sitges, you can find useful information, about how going there by public transportation works best, on this site.