Go to Google Flights, and look up flights for LHR-IAD in F (and J) one-way to get some candidates on possible options. Make a note of the ones you prefer. Then call YouFirst and ask to be put on one of these connections.
There looks to be availability in F via BOS on BA213 then connecting to a UA flight
Otherwise it looks like it's going to be tomorrow for an arrival.
If you go to YouFirst with your preferred solution, you'll almost certainly get that as long as it has seats open.