Barcelona Lost Property Office is called "Oficina de Troballes de l'Ajuntament de Barcelona." This is where all the lost and found items in Barcelona go, those found in taxis or the street are delivered to the police and they will be delivered to this office.
You can call this office to 010 if you call from within Barcelona and to this number if you are calling from overseas +34 934132031.
Their office location is in: Pl Carles Pi i Sunyer, 8 -very near Plaça Catalunya) It is good to mention that around 70% of the items delivered to the office are returned to their owners, you don't loose anything to try and if it is there they will give it to you.
If you lost a valuable item in Barcelona airport, you can contact Aena -the official airport authority in Spain. Aena has an office right in the airport in Barcelona El Prat, you need to call them and if they have found your item you can pick it up at the airport from 8 to 22h but you need to previously have arranged a day and time with the office to have someone to hand in your item.
In the new Terminal 1 (T1) building there is also a lost property office. It is located at Level 2 of the terminal building, next to the Left Luggage department.
Aena Lost Property Office: Tel: +34 93 259 6440