With respect, the Savoy, Claridges, the Connaught and the Berkley, while luxurious, are hardly hip. The following, in no particular order, are still very chic, and if it's important to you, somewhat hipper:

Blakes, The Hempel, Covent Garden Hotel, Charlotte Street Hotel, the Halkin and the Halcyon. The Met(ropolitan) attracts B list celebrities to its bar, and is a bit out of the way at Hyde Park Corner. The Sanderson and St Martin's Hotel in St Martin's Lane also fair well in the hip quotient.