The easiest way is to follow the purple signs for "flight connections." That will take you through a security check but not immigration, then back into the airside part of the terminal. The Club lounge you want is the one on the south side of the A terminal (the main building).

Depending on how much time you have between flights, and also what time you arrive, you could also clear immigration, sample the BA Arrivals Lounge (which generally has a fuller breakfast than the Club departures lounge), then go back through security to the airside part of the terminal. That is only worth doing if the immigration lines don't look too onerous; in fact, it can even be quicker to connect that way *if* there aren't too many people queued up at immigration.