Are there nonstop flights from London (STN) to Basel / Mulhouse (BSL)?

Yes. Ryanair fly this route. Flight time is about 1h 20m.

What is the fastest connection from London (STN) to Basel / Mulhouse (BSL)?

via Paris ≈ 1h 53m, via Amsterdam ≈ 2h 1m, via Nantes ≈ 2h 27m (estimated flying time, excluding layovers).

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

London Stansted Airport (STN) to EuroAirport Basel–Mulhouse–Freiburg (BSL)・707 km

Nonstop flights available (1 airline). Flight time about 1h 20m. Nonstop return flights also operate.

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

17 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.