The excavation will descend over 50 feet below the surface say reports, deeper than the height of nearby houses, and will feature a 45-foot swimming pool, hot tub, sauna, massage room, ballroom, covered courtyards, staff accommodation, parking, a turning circle and car lift.
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Police have stepped up patrols after a woman in her 40s was "dragged to the ground" in a park in east London.
Families living near Heathrow say they are supporting a group of activists facing jail for chaining themselves to the airport's runway.
Police were called to break up a "large fight" which involved a baseball bat, a man dislocating his shoulder and three arrests.