Strike action by union Unite, representing BA cabin crew, resulted in a drop in traffic of more than a tenth.
The traffic for June, measured in revenue passenger kilometers, fell by 11.1%, compared to June 2009.
There was a reduced reduction in premium traffic, however, which fell by 9.2% compared to a fall of 11.4% in non-premium traffic.
Passenger capacity, measured in available seat kilometers (ASK), fell by 8.6% over the same period, although BA said the industrial action accounted for a 5% reduction in capacity.
Despite the drop in traffic, BA said underlying market conditions continue to show improvement.
In its latest offer to Unite, BA has proposed changes "intended to address cabin crew concerns about future earning", said the airline.
The offer includes two years of guaranteed rises in basic salary from February 2011 in addition to annual increment pay increases.
BA has announced it will recruit new cabin crew, on new terms and conditions. It will deliver "a more competitive and flexible cost base", said BA.
Low cost carrier Easyjet performed significantly better in June than its full service competitor.
The number of passengers carried by Easyjet rose by 9.4% in June 2010, compared to 2009. Some 4,538,000 passengers flew with the airline last month, compared to 4,147,000 in June 2009.