LONDON — Up an alley, beyond some hoarding, through what can feel like Harry Potter’s secret portal, the underworld of an unfinished Crossrail station sprawls beneath the traffic and commotion of Tottenham Court Road. Escalator banks descend through a sleek, silent black ticket hall where towering, empty, white-tiled passageways snake toward the new, vaulted train platform, curving like a half moon into the subterranean darkness.

Crossrail is not your average subway. London’s $20 billion high-capacity, high-frequency train line, which plans to start taking passengers late next year, is billed as Europe’s biggest infrastructure project.

It will be so fast that crucial travel times across the city should be cut by more than half. The length of two soccer pitches, with a capacity for 1,500 people, its trains will be able to carry twice the number of passengers as an ordinary London subway. While Londoners love to moan about their public transit network, by comparison New York has barely managed to construct four subway stops in nearly three decades and its aged, rapidly collapsing subway system now threatens to bring the city to a halt.