So I called BA and was told that the same ticket would cost 400 percent more if bought over the phone. So I went to a BA counter in Boston and was quoted a fare that was 200 percent more than the Web-fare.
I tried booking through Expedia, but they wanted to mail me a paper ticket. Since I rarely touch down in any city for more than a couple days, intersecting with a postal-delivery system for time-sensitive materials is pretty tricky.
Then I gave up on the Web and went to SN Brussels Air, a little carrier whose website has never ever worked for me. I called the London reservations desk and booked a ticket for exactly what BA charges via its website.
That's no surprise: as it turns out, the flight is operated by British Airways. It's the same goddamned plane.
So that's the point of this post: if ever you want to book a ticket on BA from Brussels to London, book it through SN Brussels Air (by phone -- the website will probably remain busted for all eternity), and you can circumvent BA's dumbass ecommerce policies and extorionate phone/counter prices. Link