That is the beginning of the high season here. Many many people visit the city during Spring (as they should, it is beautiful during Spring) and that keeps ticket prices pretty high.
The cheapest ticket that I ever bought between DC and BA was u$s890 and that was in June of 2009. Since then with gas prices and fewer flights, the prices have gotten higher.
In my experience, the cheapest time to buy a ticket can be 1 to 3 months beforehand. At this point, if the flight is not close to being full, or if the airline is worried that it won't be full, they will try to lower the prices to gain more interest. But, and this is important to keep in mind, this is not always the case and sometimes the prices will only rise with time.
But the best thing you can do is check the prices everyday or every week until you see a price that it noticeably better than all the others have been and make your purchase then.