The routing is partially dependent on the NAT (North Atlantic Track) system on the day you fly. The NAT system is issued by the Oceanic controllers on a daily basis, taking into account the weather systems in the Atlantic. This allows airlines to plan smooth flights and make use of the lightest headwinds or best tailwinds to keep the flight on time and conserve fuel.
I won't go into a full description of how the NAT system works. Google is your friend

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Anyway, heading for Washington, this means that on departure from the Heathrow you can generally expect a "Compton" departure, which takes you west of Heathrow, over the Bristol Channel, South Wales, and Eire, to meet a more Southerly NAT track.
If the NAT tracks are more Northerly, you can expect a "BUZAD" (Leighton Buzzard) or "WOBUN" (Woburn) departure, which will head roughly North Westerly from Heathrow, passing to the East of Birmingham, through the East Midlands area, then either continuing North, following the Pennines to Scotland, or turning West, passing over Manchester, the Irish Sea and Northern Ireland.
Coming out of the NAT track usually happens somewhere off the Labrador or Newfoundland coast, and you head South West toward Washington. If the track is quite Southerly, you may route directly overhead Boston. If it's Northerly, you may pass overhead Bangor, Maine, or Albany in upstate NY. Regardless of the NAT tracks, the options eventually funnel together over New Jersey (Sparta VOR beacon), passing to the East of New York, over Pennsylvania, and joining what's called the "DELRO1 arrival" into Dulles.
This arrival passes to the north-west/west of Baltimore (so Baltimore will be out the left hand side), and you will be descending through an altitude of around 11,000ft as you pass west abeam Baltimore itself.
Fire up the map on your flight and you'll see what I mean!
Hope this helps,
Mike