FORMER President Richard M. Nixon announced last March that he would do without the Secret Service detail that has been with him since he left office 11 years ago this week.

His sole reason was to save money for the Government, according to his assistant, John Taylor.

The agency declined to give the annual cost of the Nixon agents, but based on budget requests to Congress, it was estimated at $3 million. Mr. Taylor said Mr. Nixon, who lives in Saddle River, N.J., and has an office in Manhattan, had commissioned an assessment of his security needs and would pay for a private force himself.

Mr. Nixon still has Secret Service protection. But, Mr. Taylor says, ''Within a couple of weeks, the change will take place. By late August, he is traveling to the Far East, and he will not have Secret Service protection on that trip.''

Mr. Nixon's wife, Pat, dropped Secret Service protection last year. The others on the agency's permanent-protection rolls are former Presidents Gerald R. Ford and Jimmy Carter, and President Lyndon B. Johnson's widow, Lady Bird.