Are there nonstop flights from Barcelona (BCN) to London (STN)?

Yes. Ryanair fly this route. Flight time is about 1h 54m.

What is the fastest connection from Barcelona (BCN) to London (STN)?

via Limoges/Bellegarde ≈ 2h 24m, via Paris ≈ 2h 26m, via Nantes ≈ 2h 28m (estimated flying time, excluding layovers).

from 15,000 ANA miles (economy, one way, based on the published award charts).

Josep Tarradellas Barcelona-El Prat Airport (BCN) to London Stansted Airport (STN)・1,186 km

Nonstop flights available (1 airline). Flight time about 1h 54m. Nonstop return flights also operate.

With milesANA 15,000 miles+ (via MUC)Economy, one way, estimate. Tap a connection for miles by cabin.

68 one-stop options, sorted by estimated flying time. Tap one to see the airlines on each leg and booking links.

Times are estimated from distance. Check schedules, frequency and availability with the airline or a booking site.