Well in my experience on the London Underground is that the quickest way is almost always the one that requires the least number of changes. I've tried taking shortcuts, but the extra transfers almost always eat up any time you save on a quicker route.
There are exceptions, of course - you don't want to go all the way around the Circle line, and whatever you do, don't try getting from central London to Uxbridge on the Picadilly line.
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