British Airways uses a standard 3.5mm port in all classes; you should be fine to bring your own headphones.  However, I always include in my travel electronics kit an airline headphone adapter, which allows you to use your headphones' single 3.5mm stereo jack with the double 3.5mm mono ports found on some equipment, including older BA aircraft.
In premium cabins, you may notice a smaller second outlet, and that the provided headphones have two-prong jacks. This second port is not an audio output, but a power supply for the noise cancellation system in the provided headphones. You do not need a one-prong to two-prong adapter here, and you should not attempt to plug any third party accessories into this outlet.
In fact, I'm not aware of any major carrier which has proprietary audio jacks in this day and age. You'll find 3.5mm outlets in single stereo or split mono varieties pretty much anywhere you can get electronic in-flight audio.