Unemployment in Britain, already at its worst level since the mid-1930s depression, worsened in September to a total of 2,039,003, or 8.4 percent of the work force, the government announced yesterday.

Labor Party leaders blamed Conservative Prime Minister Margaret Thatcher's economic policies for the crisis.

"The prime minister must now surely know in her heart that her policies have failed," said Len Murray, secretary general of the Trades Union Congress, Britian's affiliated labor movement.

The rise of 37,795 in September was less dramatic than in previous months, but this was due largely to teenagers who had left school finding jobs, the Department of Employment said.

The underlying trend is some 80,000 more on the dole each month.

Last month, there were 2,001,208 unemployed, or 8.3 of the 24.5 million British work force, the first time in 45 years that the jobless toll was more than 2 million.

September's 8.4 percent compares with the latest unemployment figures showing a rate of 7.6 percent in the United States, 4.1 in West Germany, 7.8 in France and 1.9 in Japan. The most recent U.S. figure covered August.

A year ago, 1.4 million Britions, or 6 percent of the work force, were unemployed. There have been successive monthly increases since.