Here are details from the Amex Platinum US site. I'm not sure if the UK has different rules.
Andrea
Receive complimentary access to participating American Airlines Admirals Club®, Continental Airlines Presidents Club, Delta Crown Room Club®, and Northwest Airlines WorldClubs® locations in airports around the world.1 Simply present the club agent with your Platinum Card, your ticket valid for same day travel on the corresponding airline that is operating the flight, and a government issued ID. Your spouse and children under age 21, or up to two traveling companions, may join you as guests in the club room.