<<The route back to London was up the west coast of Italy. My question is: who decides a flight's routing? The airline or ATC? Does it vary because the air traffic and weather varies? My return flight was a week later, but might the immediate return flight follow a different route?>>
For scheduled flights, the flight plan is stored in computer by the airline months in advance, otherwise the flight plan is filed with ATC some hours before the flight. Routes are laid down in AIPs and on various charts and these routes are what is basically flown. However, in busy airspace such as Europe, aircraft are almost constantly under radar control so the actual tracks flown depend on many factors including weather, traffic and the controller(s) dealing with the flight.