Hamsterdam was a town that was founded sometime in the Black Centuries, presumably built atop the ruins of (or a rebuilt) Amsterdam due to it's name and location (while moblising) on the official map. During the early Traction Era it became a powerful city and a fierce competetor with the likes of Paris, London and Bremen.
Hamsterdam's location on the official map.
It is not mentioned in the Mortal Engines Quartet. Some theories point to other cities which adopted known names, completely different from what they must have previously been (e.g Cidado de Roda, meaning 'city on the move' in Portuguese), perhaps Hamsterdamn, after going traction, adopted a new name.
However, before the wheeled war truly took hold and Hamsterdam was still mobilising, London consumed the still static city in a month long siege/meal the guild of historians would later call Uitsmijitter. This huge meal promptly gave London indigestion as it’s gut was swamped with materials and is one of the reasons why London had a minimal role in the Wheeled War, the other of which was that it’s second Lord Mayor, a chap named Charley Shallow, was about 'as useful as a cardboard pickaxe in a rainstorm'.
Hamsterdam after being destroyed.