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Found it: https://people.kth.se/~e95_lra/tunnelbana/bild/linjekarta.gi...
Which is to compare against the highly stylised one: http://3.bp.blogspot.com/-nSNE5wTaCGA/VDZiVonjldI/AAAAAAAAQ5...
And, well, something more realistic: https://2.bp.blogspot.com/-BPoNTy6r7UI/VDZiXCe5oEI/AAAAAAAAQ...
Otherwise you need to take the Greenwich foot tunnel, which adds a lot to the trip. It may not take 2h24min but it's about 4.4 miles, not 2.
There is a huge disconnect between underground users and walkers, I walk everywhere in London, as do most locals, mercifully the tourists and out-of-towners take the tube, unless you're going > 6/7 stops it'll take about the same amount of time.