For those needing to secure 5 flights before March and not minding a routing which seems ridiculous compared to taking Finnair direct: LHR-HEL for a weekend in January can be done for well under £100 each way, and gives options for either 2 or 3 legs in each direction with possible stops in Stockholm, Oslo and/or Copenhagen. We have booked ours for £160pp return to get all 5 flights - could have done it for £10 less if we hadn't fancied seeing all three lounges rather than coming back via one of the same. Clearly January in Helsinki is not a big seller.

To save some time searching, Tallinn and Riga both come out at only 2 legs in each direction from London - I could not force it to route via another stop, so whilst they are also good value they would only get you 4 of your required flights.