My infallible source of information BA sales, Continental Club, reports of British Airways sales being loaded as of yesterday, 14th May. Do not forget that transatlantic fares between Europe and USA can be booked on Finnair, Iberia, US Airways or American Airlines, which makes the 100 000 miles deals reported a couple of days ago an additional incentive.
Though I didn't write up on it, there's a similar offering of bonus miles by British Airways.
The fares must be booked by 4th June 2014, and the travel dates to each of the destinations vary, so you should initially screen your cities using the Low Fare Finder on BA. To truly maximise on the offer though, I suggest combining the Maximum Permissible Mileage technique with an proficiency in ITA Matrix.