My guess is YZF's company is returning him/her to London and either s/he or another paymaster then want YZF in Helsinki. That or the eligible flights rule!

T1 to T3 is quite fast, it's the same complex of buildings. There is an airside bus, but that's a bit tedious at the moment due to the constructiion work around T2. Landside is kind of a walk through a long passage way, which seems to take forever but actually isn't that far. But that route would force you to go throught the UK Border passport check. Baggage delivery is generally 20 to 30 minutes - so if you add in a 15 minute delay you can see how your time will eat away. Also BA at T3 have a special lounge waiting area which is a bit of a walk from the front of the terminal building. So all in all, not an easy connection. If all goes well it can be done in that time, but there's not much contingency. You need a bit over 2 hours for comfort really.

How about looking at a LO code share ticket on Lufthansa or even Austrian, via VIE, FRA or MUC? Or even BRU with Brussels Airline? This may get you into LHR a bit sooner and the fares are often the same as a direct LO flight. And go hand luggage only! Obviously the BA service from WAW also handily goes to T3, even if the service frequency is a bit lame.