Tonight after failing to get either of those zones, I decided to try one to the south. I wound up scoring what looks to be a perfectly serviceable if not spectacular hotel near St. James Park and Buckingham Palace for $110/night. I'm pretty happy with that.
Just to get everything out of the way, I booked a train ticket from Glasgow to London. The difference in price between first class and standard was pretty much exactly what it would cost to get wifi in standard-- it's free in first. That pretty much makes it a no-brainer.