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There are frequent flights from various UK airports to Marco Polo airport a few kilometres outside the city. Some low-cost flights go to Treviso, but the transfer time (about an hour) and hassle can take some of the enjoyment out of a family short break in Venice. From Venice Marco Polo airport to Venice itself takes 20–25 minutes by shuttle bus or about an hour by waterbus, depending where you alight. Or take a taxi or watertaxi. 

For information on getting to Venice by train, whether by the Venice Simplon—Orient-Express (which accepts kids, although is better with older ones) or by a combination of Eurostar, TGV, high-speed Italian train or Trello sleeper train, see the ever-helpful seat61.com.