Each airline develops its own noise abatement departure profiles which are then approved by the national aviation authority.
An accelerated flap retraction profile, which is generally not noise abated but more fuel efficient, allows the aircraft to accelerate to flap retraction speed, possibly as low as 200 feet AGL, get the flaps up, then fly clean at a higher climbout speed.
Most airline noise abatement profiles, however, have the aircraft climb under max lift so as to get them to 3,000 feet AGL as close in to the airport as possible, then accelerate to flap retraction speed.
Your community may have worked with BA to develop a noise abatement regime allowing the accelerated flap retraction schedule while the other airlines are flying their standard noise abatement profile. I could see that being the case if the most sensitive areas are not close to the airport but several miles out, where the accelerated profile would actually put the aircraft at a higher altitude, thus making less noise, than the standard max climb noise abatement profile.
Cheers,