London to Beijing takes about 9-10 days as of right now. You could easily get that to 5-7 days if you cut out stops (especially between Moscow and Beijing) and

London to Beijing takes about 9-10 days as of right now. You could easily get that to 5-7 days if you cut out stops (especially between Moscow and Beijing) and if you tripled the average speed of the trains from ~30-40 mph to 90-120 mph... there you go, although the latter part is what requires so much money and engineering.