The Concorde Room is only accessible to those ticketed in First Class (or the lucky few with a Concorde Room card, handed out to some of British Airways’ most frequent fliers) and is part of the Galleries South lounge complex.
While every other passenger will have to make the detour from South Security down the escalators, past the shops, and up the escalators at the end to access the lounges, those with Concorde Room access (or CCR for short), can make an immediate right and go through the single door just after security, always guarded by a staff member.
Now, about those Concorde seats. Once you're inside the Concorde Room, continue on into the lounge's boardroom, where the airplane seats have been re-purposed as office chairs around a meeting table. The room is also equipped with computers and printers for squeezing out that last bit of work before boarding.
Bonus! Once you’ve sat in the Concorde seat and had a swivel, head out to one of the other main features of the Concorde Room: its large ‘outdoor’ terrace, open to the soaring roof of the terminal above. Inside, you’ll find a restaurant with table service, a bar, a range of seating areas, and a limited number of private cabanas for little naps before long flights.
Another bonus! On the other side of the Atlantic Ocean from London, New York also offers a small chance to sit in a Concorde seat, but still within one of the revolutionary aircraft. Concorde G-BOAD sits on a pier next to the Intrepid Sea, Air & Space Museum on Manhattan's west side. Special tours must be reserved in advance, but you can and will sit in the plane for a portion of the experience. Well worth the tour's extra fee, and much cheaper than a BA First Class ticket.