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The half term school holiday will be 21 - 25 October it seems, thus the two weekends of 19/20 and 26/27 might be a bit busy, in which case might be a good idea to avoid those to have a chance of a seat on the tube. Early Christmas shoppers might be out in force then too.
Pleeeeeease make it the 11/12, it's my Brother's birthday the weekend before... but who am I hey?:)
My calendar doesn't show any UK holidays to worry about in October. FYI, Oktoberfest in Germany ends on the first weekend, October 6. People making the jump from the US might want to go to that, so having it the same weekend might not be good.
There's Columbus Day in the US on the 14th, but that doesn't really seem to matter much to folk, day-off wise or travel discountwise.
So...I'd vote for the weekend of Oct. 12 and 13th.