I recommend the Mandarin Oriental Hydepark. Itīs located near the Hyde Park - well, the name implies it - and in Londonīs best shopping area. There is a direct underground connection to Heathrow airport. You can take the taxi, of course. But donīt forget to tell the taxi driver that you arenīt a tourist...

And youīll have a great view over Hyde Park.
And itīs very "British".
http://www.mandarinoriental.com/london/
Copied from an online description:
All Suites overlook Hyde Park. Rooms overlook Hyde Park, Knightsbridge or the quiet inner courtyard. The Spa at Mandarin Oriental - recently awarded, designed by Eric Parry Architects, the therapists blend 5 different cultures into their treatments - European, Ayurvedic, American Indian, Balinese and Chinese; separate female and male heat and water oases- vitality pool, amethyst crystal steam room, solarium, colour therapy relaxation room and make up room. The Spa at Mandarin Oriental uses products from the ESPA range and Mandarin Orientals signature range of spa products. Complimentary use of latest state-of-art gymnasium, each machine has its own TV and headset, 12 pieces of Life Fitness Cardiovascular equipment. Guest Floor Manager on each floor 24 hours a day. 2 restaurants - Foliage (Michelin Star restaurant - contemporary fine dining) and The Park (all day dining restaurant).