But for Sir Terence, whose eight London restaurants include the giant Mezzo, Quaglino's and, his most recent addition, the Bluebird "gastrodome" on the King's Road, the bridge is the whole point. More precisely it was what hides beneath the bridge, before it sallies forth across the East River.
With marching pillars that rise 100ft and a vaulted ceiling clad in a jigsaw of rectangular white tiles, it is a space of majestic - and daunting - proportions. The tilework will be refurbished, gargantuan glass windows will be slotted into the outermost arches and eventually, in time for an early 1999 opening, the guts will be installed to create what should be a hive of well-heeled consumption called Bridgemarket.
The development's principal anchor will be both a Conran furniture store and, in the three bays where the pillars are tallest, the restaurant seating 320, with a mezzanine above offering covers for 100 more. Also planned is gourmet food store, not operated by Conran.
Overseeing the project is Joel Kissin, who joined Sir Terence with the opening of his Bibendum restaurant in the old Michelin building a decade ago and who is a partner in the other Conran eateries in London.
The question arises: for all his success at home, can Sir Terence bring his formula - giant spaces, painstakingly self-conscious design and expensive fare - to a city where no fewer than 265 restaurants joined the fray last year while, more worryingly, 129 closed their doors?
The omens so far have not all been good. The Bridgemarket development itself nearly died at conception because of opposition from local residents who feared for the architectural heritage of the bridge. The quarrelling only subsided nine months ago when the city's Landmarks Preservation Commission finally acquiesced to the $16m (pounds 10m) project.
Nor will the concept of a stadium restaurant with seats for so many necessarily impress blase New Yorkers. The last two months alone have seen the birth of two high-profile dining houses, the Globe on Park Avenue South and the super-acclaimed Balthazar, owned by a long-established Brit restaurateur in the Apple, Keith McNally. Both have room for almost 300.
Meanwhile, Sir Terence comes to the project with some unhappy baggage that goes beyond Britain's unconvincing image as a country of gastronomy.
When he lost control of the Conran furniture stores that he used to run in New York and other US cities in the late 1980s, they were offering products that, bluntly, were not of the highest quality. The shops limped into undignified liquidation in 1994. Thus, while the Conran brand in Britain may be gold, in the US it is somewhat dog-eared.
Mr Kissin, however, is all optimism. "In two years, all of that history will be erased from peoples' memories," he asserts. Nor does he have any fear that the Conran restaurant will join the ranks of the quick-to-open- even-quicker-to-close in New York. "It is true that restaurants can fail quickly in New York, but as long as the quality is good they will last a long time."
Bruce Hanks, another Brit who is a partner in The Independent, a sizzling hot bistro in Tribeca unrelated to this publication, admits that the location is "interesting". The nearest establishments of renown are several blocks to the west in the Madison Avenue corridor. But Mr Hanks admits that may not be a drawback if Conran can imbue his Bridgemarket with enough style and excitement to make it a new destination for diners. "New Yorkers love that - when they go out to eat in a place that is stylish. In fact, I think Conran will do fabulously."
There are some things about operating in New York that Conran restaurateurs will have to adjust to. They range from the city's tough tobacco laws, forbidding cigarette smoking in all but the tiniest restaurants, to translations on menus. First course will become appetisers, aubergine-eggplant, coriander- cilantro.
Already Mr Kissin has come up against one of the ogres of doing business in America: the absolute necessity of decent liability insurance and the incredible cost of the premiums. "I wonder if Americans have any idea how much extra they pay for everything because of the insurance," he muses.
There are some changes that Mr Kissin is looking forward to, however, including, he says, the diners themselves who, he explains, know the rules. They leave a 15 per cent tip if they are satisfied with the service and withhold the tip and speak up when they are unhappy.
Sir Terence can only pray, meanwhile, that the surge of prosperity and free spending that has buoyed New York over recent months, due in part to the helium-balloon performance of Wall Street and the impact on crime wrought by its tough-talking mayor, Rudolph Giuliani, does not fade before 1999.
If it does not, and if Sir Terence and Mr Kissin get the ingredients right, the restaurant under the bridge could crash the city restaurant scene with spectacular aplomb. Then, Sir Terence has hinted, he will open elsewhere in the city. Perhaps, even, down in Soho or Tribeca.