Britain's unemployment rate fell to a seasonally adjusted 8.4 percent in June from 8.6 percent in the previous month, while industrial production rose 0.6 percent in May, the government said Thursday. The unemployment rate also was down from 10.4 percent in June 1987, the Department of Employment said. However, the department said half the decline in the latest month was the result of a new definition of employment. People employed by government job training programs now are being counted as employed. The new practice brings Britain more in line with other European countries' methods of defining employment and adds about 334,000 persons to the ranks of the employed, the department said. Total seasonally adjusted British unemployment came to 2.38 million people in June, down from a revised 2.41 million people in May and 2.92 million people in June 1987, the department said. Meanwhile, industrial production was up 3.8 percent from a year earlier, according to the Central Statistical Office. The latest figures compare with April's revised 1 percent month-to-month rise and 4 percent year-to-year rise. The office said the index of industrial production, which uses a 1980 base of 100, rose to 116.7 in May from a revised 116 in April and was up from 112.4 in May 1987.