Heathrow is the largest UK airport - and a number of carriers fly direct to Washington. However I usually fly to the USA's capital from Birmingham International. This avoids going into Central London or using the M25. Sadly there is no direct flight - but the avoidance of the hassle at Heathrow or Gatwick makes it worthwhile. If you fly into London (or are travelling from the UK to the USA), it's worth giving thought to Birmingham.
The West Coast line serves Birmingham International railway station. Although technically outside the airport perimeter - it is closer to the terminals than many so-called airport railway stations. SkyRail links the station to the airport terminal. It is free, operates about every 2 minutes when the rail station is open and the journey takes less than 2 minutes. Fast trains take 90 minutes to London Euston (Virgin) - other places are served by London Midland and Cross-Country Services. It's very easy for me in Milton Keynes - direct trains from both Virgin and London Midland; Direct coaches from the newly opened coachway; and by car straight up the M1 and M6.
The quickest route to Washington DC is via Newark by Continental. (CO27)
All possible routes are outlined here.
Other Airport websites
London Heathrow
London Gatwick
Manchester