In London, footways and pavements are generally for pedestrians only. Local authorities and TfL can issue Penalty Charge Notices if a motor vehicle is left on the pavement where it isn't explicitly allowed.
Some boroughs provide dedicated motorcycle and scooter bays both on-street and in car parks. These are usually signed and road-marked, and may be free or paid depending on local policy.
Red routes, bus stops and cycle lanes have additional restrictions. The safe rule is: if there isn't a marked bay or clear signage permitting parking, don't leave your Vespa there.
This page is neutral and factual. It isn't legal advice; always check the latest official guidance and local signage.