Documents leaked apparently by angry defense officials here show that the British Treasury has proposed substantial cuts in the country's planned military spending over the next three years which would undermine its commitment to meet NATO targets for increased defense outlays.

The documents are diplomatically embarrassing both to Prime Minister Margaret Thatcher, whose government has promised adherence to a 3 percent NATO-wide annual increase, and to the Carter administration, which proposed that goal for the alliance in 1977 and has considered Britian a bulwark of compliance. The British Treasury has put a lid on such defense spending for the rest of this year and has recommended that more than $1 billion be cut from planned increases over the next three years.

Thatcher could still override the Treasury's recommendations, but defense officials have acknowledged that the 3 percent target is unlikely to be met this year.

Earlier, the Thatcher government had trumpeted its commitment to the full 3 percent defense increases as evidence of its strong loyalty to U.S. leadership in the North Atlantic Treaty Organization.

[The White House and the Defense Department refused to comment on the evidence of changes in British military spending.]

American officials have pointed to the example of Britain in trying to prod West Germany and -- outside NATO -- Japan to raise their defense budgets. Despite sometimes pressure from Washington, the smaller NATO nations Denmark, Belgium and Holland are falling short of the proclaimed goal.

Until now, Thatcher has exempted defense from her monetarist economic policy of bugetary cutbacks.

But the recommendations of Treasury, leaked yesterday, could mean that Britain's defense spending would rise by only half the 3 percent NATO target through 1984, although Thatcher's defense Secretary Francis Pym said today that final decisions have not yet been made.

Defense officials and military commanders are fighting the Treasury's spending restraints in a bureaucratic battle that became public with the leak to Britain's domestic news service, the Press Association, of the secret government documents revealing not only the Treasury's plans but the military's objections. Pym has acknowledged the authenticity of the documents and begun an investigation into their leak, which violates Britain's draconian Official Secrets Act.

In a confidental letter to Pym last month, Thatcher's top budget cutter, Treasury Chief Secretary John Biffen, said defense must now "accept a fair share" of new, across-the-board spending cuts because of the country's "acute economic difficulty." Biffen told Pym that "clearly this would mean that we would not meet the 3 percent target."

Thatcher's pledge to reduce government spending during Britain's economic crisis apparently may now be given precedence over the commitment to meet the NATO target. "A strong defense requires a strong economy," Biffen wrote to Pym in mid-September.

But the Defense Ministry's top civil servant, Permanent Undersecretary Frank Cooper, warned Pym in a secret memo a few weeks later that Britain's military chiefs on staff were "naturally seriously concerned" about the effect the reductions would have on operations and weapons buying

Even before Biffen sent his letter recommending the new cuts, the military chiefs complained to Cooper at a meeting in August, according to another secret memo, that they were being given too little money for major weapons programs.

Pym then said at another meeting two days later, according to the documents, that he "could not rule out the option of slower progress towards plans to improve manning levels in the Army over the next few years."

Britain's chief of staff, Adm. Terence Lewin, responded that the military chiefs would prefer to review Britain's overall defense commitments instead. Present and former defense officials had previously warned that Britain's participation in NATO deployment might have to be reduced to afford the $12 billion for replacing Britain's multiple warhead Trident submarine-based nuclear missile system. The recently reduced Trident program remains protected from further cuts in planned defense spending.

Pym has already ordered minor changes in Britain's military deployment, reducing the cruising speed of British ships on NATO duty in the Mediterranean to save fuel, pulling two British frigates out of a NATO exercise and cancelling joint exercises with Danish forces, according to the documents.

Cooper warned Pym in a confidential memo two weeks ago of "evidence of more NATO and international awareness of our reduction in activity levels" at a time when the "international situation had deteriorated dangerously" because of the Iraqi-Iranian war.