BA are flying LHR-TLL twice weekly on Tue and Sat from March.
Surprising choice and frequency! Tallinn Airport website (in Estonian:
Tallinn-Londoni liinile lisandub uue vedajana British Airways - Tallinna Lennujaam ) hopes it might be useful for business travellers, which is a bit hopeful (or cute). Up against Ryanair (4xweekly) and EasyJet (2xWeekly).