DME Procedures
When you exit pier, you normally turn lfet, and keep left, (right is for Russians), if the hall is busy, try to stay slightly left of centre, as theis line serves 3 or 4 desks.
Get your form filled in on board, and present with a slight smile.
The bagage belt is usually the one slightly right of centre as you enter the reclaim area. Often not signed. The delay can be very long, so dont fret if the immigration is slow.
Usually exit via the nothing to declare line, but the customs often stop shuttle traders.
Then the fun starts: IF POSSIBLE get your hotel to send hotel car. they will have signage for you. If takign a local taxi, up to 100US$....beware.
There is a overground train into the city, and there are shuttle bus's to the nearest metro station.
Allow 2 hours for taxi to centre.
I have taken 30 mins just getting out of car park, so be patient.
Have a great time in Moscow.
For the return both Swiss and BA have very nice exec lounges, and the fast track departure clearance (entrance is just to the left of the normal exit), might be slower than the normal.
Yes, it is often slower to clear inbound at T1 LHR, than DME.
Good luck.