Are there nonstop flights from London (LGW) to Sofia (SOF)?

Yes. easyJet, TUI Airways fly this route. Flight time is about 2h 52m.

What is the fastest connection from London (LGW) to Sofia (SOF)?

via Stuttgart ≈ 3h 22m, via Munich ≈ 3h 22m, via Frankfurt am Main ≈ 3h 23m (estimated flying time, excluding layovers).

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

London Gatwick Airport (LGW) to Sofia Airport (SOF)・2,012 km

Nonstop flights available (2 airlines). Flight time about 2h 52m. Nonstop return flights also operate.

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

60 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.