Did Britain control the east coast of Washington?

If you are referring to the british invasion of the east coast of Washington D.C, then you are correct. In the very early 1800's British forces invaded and burned down the White House in Washington D.C. The president had to flee for his life. Fortunatley for the US, a hurricane came along and messed with the British supply lines and forced them to retreat back to their ships, preventing them from marching further inland.