score:10
Rail travel didn't start in Germany until 1835, which I believe is after the period described in the book. Steamships also were not available at that time, so travel in 1800 is not by steam, but by horse and sail.
Travel by horse is generally at the rate of 30 miles or 50 km per day assuming a normal pace. Amsterdam is about 450 km from Frankfurt, so your looking at nine days of travel best case just to reach a port. But this would have required crossing many borders, especially since Germany wasn't unified at the time, so it's perfectly reasonable to assume two weeks as the normal travel time. Given that, plus the time required just to arrange ocean travel, wait for decent winds, etc., three weeks from Frankfurt to London is very reasonable for normal, non-rushed travel.