Are there nonstop flights from Leeds (LBA) to Tallinn (TLL)?

No. The fastest connection is via Copenhagen, about 3h 5m of total flying time.

What is the fastest connection from Leeds (LBA) to Tallinn (TLL)?

via Copenhagen ≈ 3h 5m, via Riga ≈ 3h 16m, via Amsterdam ≈ 3h 17m (estimated flying time, excluding layovers).

Leeds Bradford Airport (LBA) to Lennart Meri Tallinn Airport (TLL)・1,719 km

No nonstop flights. The fastest connection is via Copenhagen (CPH), about 3h 5m of flying time (layover not included).

None.

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