A Canadian life insurance company, following its business across the border, has moved its U.S. headquarters to Alexandria, hoping to heighten its corporate presence here and further increase its share of the U.S. life insurance market.

Crown Life Insurance Co., which already does more than half its business in this country, moved into the Torpedo Factory in Old Town last month. The company's group insurance division, the first to move to Alexandria, will employ 70 people, mostly Americans. Ranked in the top 2 percent of North American life insurance firms, Crown has $52 million in insurance policies and assets of $3.7 billion.

The Canadian company, founded in Toronto at the turn of the century, has operated in the United States since 1924. The firm, which has 100 branches across the country, earned 62 percent of its premium income in this country last year.

Crown also has two wholly-owned subsidiaries, American Crown Life Insurance Co. in New York and Private Ledger Financial Services Inc., which sells a broad range of investment-related products.

Crown, with 21,600 employes, also has foreign subsidiaries in Britain, Hong Kong and the Caribbean Islands and says it has more than 5 million clients worldwide.

Robert A. Bandeen, the company's president and chief executive, says he has little faith in government efficiency and is a leading proponent of the movement to deregulate the Canadian insurance industry. If adopted, deregulation proposals would allow an expanded offering of diversified financial services and "one-stop financial shopping" for investors, a trend patterned on recent shifts in the American insurance industry.

"We're a long way from a one-stop financial shop now," Bandeen said recently. "But, we're moving in that direction."

Bandeen, who says he is a "private enterpriser" at heart, was formerly the president of Canadian National Railways. His tough management style is credited with turning around Crown Life, which reported a profit in 1983 that was about five times what it earned the previous year.

Crown Life, which offers life and health insurance, pension programs and reinsurance services to other insurance companies, had revenue of $1.2 billion in 1983. It is part of Crownx Inc., a Toronto holding company whose other divisions are in the financial services and information technology businesses. Another subsidiary, Extendicare, North America's fourth-largest provider of nursing care, runs clinical laboratories, mobile health units and 165 nursing centers.

Life insurance policies in the U.S. are sold through independent agents who are not employes of the company. Bandeen said that the arrangement gives the company a certain degree of flexibility that it doesn't have in Canada.