Are there any previous cases of the UK intercepting and arresting a US citizen traveling through Europe for something that isn't a crime in the US?
Extradition treaties, such as the UK–US Extradition Treaty of 2003, allow for extradition requests between the two countries.
They generally require that the alleged offense be a crime in both jurisdictions ("dual criminality") which ensures that individuals are not extradited for actions that are not considered crimes in their home country.