Sir Nicholas Henderson, who will become Britain's ambassador to the United States next month, has criticized sharply the British governments since World War II for allowing the nation to fall into serious economic and diplomatic decline, according to a document leaked to the press.

After serving as British ambassador to West Germany from 1972 to 1975 and then to France until early this year, Henderson concluded that Britain had fallen far behind those countries. He blamed Britain's demise on its loss of a national will to succeed, on its "lack of professionalism" in business management, on obstructionist labor unions, and on foreign policy failures, particularly the nation's inability to take advantage of the Common Market.

"You only have to move about Western Europe nowadays," Henderson observed, "to realize how poor and unproud the British have become in relation to their neighbors."

Henderson's unusually severe scolding of his own government, accompanied by an urgent plea for it "to do something to stimulate a sense of national purpose" before it is too late, was made in what he thought would be his farewell dispatch from Paris when he retired as ambassador to France at age 60 on March 31. It was labeled "confidential" and sent directly to David Owen, foreign secretary in then-prime minister James Callaghan's Labor government.

But after new Conservative Prime Minister Margaret Thatcher asked Henderson last month to come out of retirement to go to Washington someone in the Foreign Office here leaked the lengthy document to The Economist news magazine, which published most of it today. Henderson's undiplomatic critique of Britain and its leak to the press were both very rare here.

The Foreign Office and the prime minister's office refused to comment on the document, except to say that Henderson, a career diplomat, would still be going to Washington. There also will be an investigation to try to find who leaked the confidential dispatch, which in Britain could be a violation of law. The Economist said only that it did not come from Henderson.

Thatcher's foreign secretary, Lord Carrington, undoubtedly saw Henderson's dispatch when he took over at the Foreign Office last month, before Henderson was selected for the post in Washington. The view Henderson expressed actually are so close to Thatcher's beliefs about Britain's decline and what needs to be done about it that a British Braodcasting Corp. radio commentator today said Henderson apeared to have "written himself a job application."

But Henderson, known in the Foreign Office for his nonconformity, sent the dispatch before the election to a Labor government likely to disagree sharply with his opinions bout labor unions or the Common Market, among other things.

In his dispatch, Henderson compared the failure of recent British governments to inform the public of "how far Britain's economy had fallen behind that of our European neighbors" with "how little the British governments of the 1930s did to englighten the British people about the rise of Nazi Germany."

Henderson said in the dispatch that if those who read it thought it went "beyond the limits of an ambassador's normal responsibilities, I would say that the fulfillment of these responsibilities is not possible in Western Europe in the present uncertain state of our economy and our European policy."

He said he recognized that Britain's relative industrial declineactually began a century ago after abosrbing shocks from the loss if its empire and the strain of two world wars.

His prescription for the future is strikingly similar to Thatcher's and Carrington's: Become a more willing and imaginative member of the European Economic Community and its currency-management system while working more effectively from the inside to get Britain a better deal than it has now.

The United States, Henderson argued, always has promoted European unity, so a better British relationship with the rest of Europe would improve not harm its "special relationship" with Washington. CAPTION: Picture, SIR NICHOLAS HENDERSON . . . secret document cites decline