The best way of tackling this I can think of with ITA is choosing the "any airport within 300 miles" option
for London, that would include DUB,PAR,BRU,AMS

it takes a while to process but for your dates it comes out with
$671 IAD-LHR on BA as the cheapest option...if you scroll further down, there are options to BRU,AMS,CDG, and a combination of cities