BRITAIN'S largest exporter and defense contractor is having to devise an emergency strategy to head off a potential takeover.The company, British Aerospace (BAe), has said profits will be sharply lower than expected this year, due to problems in its automobile and real estate businesses, as well as in defense and commercial aircraft. The troubles at BAe led to a recent boardroom coup that forced the resignation of its chairman, Sir Roland Smith. The coup sparked claims by figures in London's financial community that BAe is not viable in its present form and should get rid of its Rover Group, Britain's last locally controlled volume carmaker, and some other operations. Since some of the potential buyers are foreign companies, an attempted takeover could evolve into a political fray. Gordon Brown, the Labour Party's trade and industry spokesman, said the company's crisis underlined "the unwisdom of having privatized this vital part of our defense industry." BAe was privatized in two stages by the Thatcher government in 1981 and 1985. The company took over Rover in 1988. A key figure in the bid to shore up BAe's defenses is the Canadian-born Sir Graham Day. He has taken over as BAe's interim chairman. Sir Graham has pledged to stay at his post for at least a year while a search for a permanent chairman goes on. He confirmed last week that since Sir Roland's resignation, there had been a lot of interest shown by companies wanting a stake in BAe. He declined to name the firms. Financial sources indicated, however, that Sir Michael Richardson, chairman of the brokerage house Smith New Court, was behind an early, abortive bid by a consortium to acquire BAe and sell the Rover subsidiary. Sir Michael, the sources said, figured that BAe was highly vulnerable and that to have a future it would have to shed some of its activities. Within 72 hours of Sir Graham moving in as BAe chairman there were widespread reports that Lord Weinstock, chairman of the British electronics giant GEC, and a major BAe customer, was prepared to form what one source called a "defensive alliance" with the company and buy 15 to 30 percent of its shares. British government officials said privately that they favored such a move by Lord Weinstock, since without it BAe would be "prey to foreign predators." Among foreign companies said last week by City of London sources to be interested in acquiring a piece of BAe was Deutsche Aerospace, owned by Daimler Benz, Germany's largest company. Deutsche Aerospace, like BAe, is part of Europe's Airbus consortium, which makes commercial aircraft. THE extent of BAe's crisis began to become public in September when the Financial Times reported a secret plan to raise $746 million in a rights offering to shareholders. Then Sir Roland announced that profits for the year would be $255 million - half what investors had been expecting. BAe shares took a nose-dive, putting pressure on Sir Roland to take the blame and resign. In fact, BAe's problems go back a long way. The company was the product of a 1977 shotgun marriage of the aircraft divisions of several private companies. In 1986 Sir Roland initiated a strategy of diversification, ordering the takeover of Royal Ordnance, the arms manufacturer, the Dutch contractor Ballast Nedam, and the property company Arlington Securities. The Rover Group acquisition was part of this strategy, as was property development based on the sale of large amounts of real estate owned by Royal Ordnance. For the past year, however, the British real estate market has been in the grip of a major recession. The company's prospects have not been helped by the collapse of communism and the consequent review worldwide of defense requirements. In the first half of this year British car sales fell 20 percent. Two months ago BAe decided to abandon attempts to sell its Rover 800 in the United States. Also, BAe executives admit that the bad state of the airline industry in the US sets limits on sales of the company's commercial aircraft there. With a general election expected early next year, Prime Minister John Major does not want any part of the controversy that would be sure to swirl around an attempt to sell off BAe's car group, which employs 35,000 workers. Last year the Japanese carmaker Honda bought a 20 percent stake in Rover.