To D, a few steps outside after exiting near gates 15/16 of terminal A (with a roof over your head and past an old-train-turned-snackbar). Terminal D is tiny and does have central checkin and security for all (bus boarding) gates. Unless you're on the mid-day LCY flight, it may be a bit of a zoo (for TXL, if you're used to LHR T5 it's nothing). BA lounge is upstairs just before you exit A towards D.

​​​​​​​Edit: oops, cross-posted with cws' comprehensive info, so just keeping the extra bits.