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The Conde Nast brand will run the space, which is normally occupied by boutique patisserie L'Orchidée, over the summer until 25 September.
The café serves specially created Vogue 100 champagne cocktails and a Vogue 100 punch, as well as a traditional English afternoon tea.
Alexandra Shulman, editor-in-chief of British Vogue, said: "2016 is an exceptional year for Vogue, and continuing the centenary celebrations the Vogue Café will be a perfect stop-off for shoppers in The Village at Westfield."
The pop-up showcases a range of legendary British Vogue covers from the last century while the menu features macarons, sandwiches and sweet treats.
The brand also marked its centenary at its annual Vogue Festival,
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