The reason I'm asking is because of Washington D.C.'s location. It wasn't easily accessible by land and it wasn't easily traveled to by waterways. In what battles were the British able to get to Washington D.C. to burn down the White House?
British Major General Robert Ross landed his brigade on 18 August 1814 at Benedict, Maryland, less than 40 miles (65 km) from Washington DC. The Royal Navy had blockaded Chesapeake Bay since spring 1813, and the US had built the Chesapeake Bay Flotilla for protection; this was trapped in the Patuxent River, enabling the British to land.
The only significant battle was on 24 August at Bladensburg, about 9 miles from Washington DC, where Ross defeated a larger force of US militia under Brigadier General William H. Winder.
He then immediately proceeded to Washington DC and burnt the White House, Capitol, Navy Yards and other public buildings that night in retaliation for the earlier burning of Toronto (then called York) and other Canadian towns.
Ross then joined the wider British attack on Baltimore, but died in the Battle of North Point on 12 September.