I don't know about individual carriers, but by airport the figures for January are
Heathrow-USA: +0.7%
Gatwick-USA: -3.7%
Manchester-USA: +1.2%
All UK Airports-USA: +0.4%
I guess that could be called flat.
EI transatlantic figures (for February, so not like with like) were up 10%, which isn't too bad in comparion, although to what extent that is driven by giveaway seats when the load is so bad must be open to question.