The distance has not stopped him from trying, on two occasions, to outfit the home with king-size air-conditioning units, an unusual amenity in rainy London. The plans have faced resistance. Giulia Marsan, a descendant of the founder of Fiat, who lives next door to Mr. Bloomberg, told the local planning board she would “strongly object” to the units, citing noise concerns. An environmental officer agreed; the board later rejected the plans.

Ms. Marsan, in a brief interview, said she barely saw Mr. Bloomberg in the neighborhood. “That’s the hope for everybody in Cadogan Square,” she said. “You never know what’s going on with your neighbors.”

On his visits, Mr. Bloomberg enjoys dining with London celebrities. He has eaten at Le Gavroche, a luxury French restaurant, named for a street urchin in “Les Misérables,” with a $280 tasting menu. On one trip, he hosted a dinner with Louis B. Susman, the American ambassador; Kevin Spacey, the actor; George Osborne, the chancellor of the Exchequer; and Honeysuckle Weeks, a young English actress Mr. Bloomberg admired.

Ms. Weeks later gushed about the “special dinner” to The Daily Mail. Mr. Bloomberg was less impressed: he was disappointed when he learned she smoked.

‘It’s Not a Timid Building’

Mr. Bloomberg has long sought a place on the map — literally. Years ago, there was talk that he wanted to rename Finsbury Square, site of his company’s office, after himself.

He ended up getting another square instead.

Bloomberg Place, soon to be enshrined on the London map, is currently a mud pit crawling with cranes and bulldozers. By 2016, it will be home to a futuristic campus designed by the architect Norman Foster: it is to include a pair of undulating office buildings, pedestrian plazas, spaces for 390 bicycles and, if the mayor gets his way, branches of New York restaurants.

“It’s not a timid building,” Mr. Foster said, on the phone from his home in Switzerland. “It will leave a large impression on London.” (Some neighbors are less generous, calling the development “a bulky, impenetrable mass.”)