It is true that passengers (including myself) often transit to North America (not just New York) via Heathrow. But it looks unlikely to become a problem. UK will most certainly resettle bilateral agreements with the USA and Canada - if only because AA, DL, UA and AC all have extensive operations at Heathrow and in the UK in general.
Likewise, British and EU carriers will most certainly retain their existing rights to fly between the UK and the EU. The biggest concern for airlines is the EU ownership rule, especially for IAG.
Since Finnair does not fly out of the UK to non-EU destinations, I don't really see the problem? Is there a concern that the transatlantic cartel will lose its immunity, or what? Or is it an indirect anticipation of IAG problems having ripple effects on Oneworld?