Another thing to be aware of is that the SEA-LHR BA flight is the only direct flight between the two cities, so it tends to be popular. (I work for the London office of a Seattle-based organisation, so know the route well.) For travelling over the summer, I'd expect you to need to book a good time in advance and be flexible with dates. Alternatively, you could fly out of a different airport, but if you're going to do that it's probably cheaper, and no mre difficult, to redeem the miles on AA, as previously suggested.

And welcome to FT.