That clout has been hard won for an industry that was struggling not so long ago.
Britain always had a flair for car design, producing such classics as the Jaguar XKE and Austin-Healey Sprite. But the industry in the 1960s and 1970s suffered from underinvestment, dated models, poor quality and frequent strikes.
The outlook began to change in the 1980s, as Japanese automakers began to look for a foothold in Europe to gain access to the single market. Britain beckoned. Under Prime Minister Margaret Thatcher, it was increasingly welcoming to foreign investment, unions were in retreat, and Britain's own auto industry was not much of a competitive threat.
Toyota came in the early 1990s, finding a large site in central England that could be cleared and built to the company's specifications. The Japanese companies brought efficient production methods.
“The Japanese completely reversed what was going on,” said Garel Rhys, a professor emeritus of motor industry economics at Cardiff University. “They showed that Britain was not a place that was out of control.”
The Japanese carmakers brought a more team-oriented approach to once-contentious British manufacturing. Workers at the Toyota plant, who make more than 30,000 pounds on average a year ($37,360), are called “members.”
Toyota's collegial approach has helped with labor relations at the plant, which is unionized. Toyota says it has lost no time to strikes in about a quarter-century of manufacturing in Britain.
“The main reason is their philosophy,” said Mr. Tsouvallaris, the union representative. “There is always a channel open for communication.”
Other automakers soon followed their Japanese rivals.
In the early 2000, BMW of Germany began building a new line of Mini cars in Oxford. Later that decade, Tata of India took over the old British brands Jaguar and Land Rover.
It has helped grease Britain's economy.
Over all, the country made about 1.6 million cars last year. The figure, though much smaller than in powerhouses like the United States and Japan, leaves it roughly level with France as Europe's third-biggest automaker, after Germany and Spain.
The industry is now plagued with uncertainty.
The British prime minister wants to start negotiations in early 2017 on the terms of the country's exit from the European Union, talks that could last two years or more. The spectrum of possibilities is broad, from Britain remaining part of the single market to the country facing high barriers to trade with the Continent. Both sides have their own competing interests with carmakers, putting the industry in the middle of a potential fraught negotiation.
“The car industry really did take the prospectus of the E.U. at face value,” said Stephen Adams, a partner at Global Counsel, a political risk firm in London. “It relies on the free circulation of goods in the E.U. not just to sell products but to make products.”
Toyota has options if the Burnaston plant ultimately proves unprofitable.
The carmaker has more than 30 vehicle manufacturing plants around the world and, like many of its rivals, pits them against each other to bid for the right to make various models. Toyota also has a string of plants across the region, including large car-making hubs in France and Turkey.
The company has had to trim operations at Burnaston before, closing an assembly line in 2010. Annual production is down to 180,000 from a peak of 282,000 in 2006.
Mr. Walker, the Toyota executive, says a new model for Burnaston is under consideration, although no decision has been made. The plant has already handled several changes to models in its history. On display in the reception area is the Avensis, versions of which are exported to Japan.
“This is the only plant in the world that sends cars back to Japan,” Mr. Walker said. “We are very proud of that.”
