Are there nonstop flights from Rome (FCO) to London (STN)?

Yes. Jet2.com fly this route. Flight time is about 2h 12m.

What is the fastest connection from Rome (FCO) to London (STN)?

via Milan ≈ 2h 42m, via Genova ≈ 2h 42m, via Turin ≈ 2h 42m (estimated flying time, excluding layovers).

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

Rome–Fiumicino Leonardo da Vinci International Airport (FCO) to London Stansted Airport (STN)・1,442 km

Nonstop flights available (1 airline). Flight time about 2h 12m. Nonstop return flights also operate.

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

79 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.