British Prime Minister James Callaghan announced today what appeared to be significant progress in efforts to persuade India to accept full international inspection of its nuclear installations.

India, which exploded its first nuclear device in 1974, has refused to sign the Nuclear Non-Proliferation Treaty, curbing the spread of nuclear weapons and only last week, President Carter failed in his attempts to persuade Indian Prime Minister Morarji Desai to sign the accord.

Today, Callaghan said that Desai has agreed to allow full international inspection of all India's nuclear facilities once the United States, Britain and the Soviet Union agree on principles of a new comprehensive test ban treaty, which Callaghan said could occur later this year.

India is still refusing to actually sign the non-proliferation treaty, Callaghan said, adding, however, that "I do not regard (that) as absolutely essential to the problem" of insuring that India does not in the future use its nuclear capabilities for non-peaceful purposes.

Inspection of Indian facilities by international experts would theoretically insure that India could not again secretly prepare a nuclear device without the world knowing about the preparations.

In his talks with Callaghan, Desai appeared to have made one significant concession. The Indian premier apparently is no longer insisting that China and France sign a comprehensive treaty, which would pledge its signatories to ban all nuclear tests.

France and China are not participating in the Geneva talks on the treaty and Desai had been saying that India would probably not agree to inspection of its nuclear facilites until the five major nuclear powers signed a comprehensive treaty.

(In Washington, an American official said the Indians previously had not been precise about whether China and France would have to sign a comprehensive treaty before India would allow its facilities to be inspected. The American official said Desai's position, as reported by Callaghan, appeared to represent some advance in the Indian position.)

Callaghan, who is now in the middle of a 10-day tour of the Indian subcontinent, seems to have managed to persuade Desai that to wait for France and China to sign a test ban treaty would be quite impractical. Desai had assured the United States that India has no intention of exploding a second nuclear device even before today's agreement on future inspections on India's nuclear facilities.

Callaghan also told Desai that, from British-American contacts made only last week, it now seemed possible that the United States, Britain and the Soviet Union could come to some agreement on a comprehensive test ban treaty and on a scheme for the reduction of their nuclear armaments by "the end of 1978."

Desai said that such a treaty, even if a limited one, would satisfy his demands for opening up Indian nuclear facilities for international inspection.

It would thus seem probable, if Callaghan is correct with his timetable, that Desai could open all his atomic projects up to inspection by the Vienna-based International Atomic Energy Agency by the beginning of 1979.

But now the key question, from the Indian point of view, is whether the U.S. Congress would view India's concession as sufficient to enable supplies of U.S. enriched uranium for the Tarapur reactor, near Bombay, to continue.

Legislation already in the pipeline in Washington threatens these supplies if India fails to sign the non-proliferation treaty. At a press conference in Delhi last week, Sen. Abrabam Ribicoff (D-Conn.), one of a five-man team from the U.S. Senate visiting the region, promised that the Tarapux fuel supply would be cut off "without a doubt" if India continued to refuse to sign.