The best way of not getting something is never to ask, so good luck.
I'm sure you know this, but the best route to success is to align yourself with a corporate responsibility objective, far more than offering to play in a lounge or a few freebies which have minimal effect. The maximum benefit to BA is if they can get good feelgood PR, so you need to scour what they do with other groups in similar contexts and see what they like to support and what use they make of the sponsorships in PR material.