Long accustomed to bad economic news, Britons learned today that their inflation rate is falling, their trade gap narrowing and interest rates dropping.

But industrial production - down to scarcely above the 1970 level-provided a gloomy counterpoint to the other government figures. And the stock market declined as the international trade figures fell short of financial world hopes.

"It looks as though we are over the worst," Employment Minister Harold Walker said as he reported retail prices were up only 0.1 per cent from June to July, although 17.6 per cent higher than a year ago.

The index has risen nearly 84 per cent since January 1974, and Britain's inflation rate is one of the highest in the industrialized world.

Citing a sharp fall in the six-month inflation rate - from 9.3 per cent in June to 6.6 per cent in July - Walker said it was a "reward for restraint" by labor over pay increases, and the predicted "steady progress" toward the government's year-end goal of an annual inflation rate of 12 per cent.

Meanwhile, the gap between Britain's earnings from other countries and its spending abroad diminished to a deficit of 36 million pounds ($63 million) in July from 81 million pounds ($141.75 million) in June.

But that disappointed some financial observers who had predicted Britain would come out of the red to the tune of a 150-million-pound ($262.5 million) surplus.

An even larger deficit in "visible" trade - 256 million pounds ($448 million) against June's 301 million pounds ($526.75 million) was offset in the overall total by Britain's usual surplus in the "invisibles" of tourism, insurance, shipping and the like.

July exports were put at 2.714 billion pounds ($4.749 billion) and imports of 3.077 billion pounds ($5.384 billion).

Government officials cited a fall-off in diamond trading, high imports of cars and raw materials and slowness of an expected increase in tourism earnings as reasons for the disappointing results.

An inflow of foreign currency to Britain, banking on economic recovery and North Sea oil-fed prosperity, was behind the drop in the Bank of England's Minimum Lending Rate (MLR) from 7 1/2 per cent to 7 per cent - the lowest in the five years since it was substituted for the old Bank Rate.

The rate also was cut by a half-point Aug. 5 and now is at its lowest level since it was officially formulated five years ago. Late last year, the rate stood at 15 per cent.

The MLR - the lowest rate at which the Bank of England lends to other banks influences the rise and fall of other bank rates, and last week's MLR cut sparked a general reduction of base lending rates by Britain's major banks. But there was no immediate indication when, if or how much the latest lowering of the MLR would be passed on to bank customers.

Said a spokesman for National Westminister Bank: "We shall be taking a long, cool look at the situation over the next few days."

Meanwhile the heart of Britain's economic problems - stagnant industrial production - provided no hope.

More than 1.5 million workers have been idled by industrial slowdowns, the highest number since World War II, and the government said Friday that industrial production declined 3.7 per cent in June from a month earlier.

A government economist said the sharp fall was due to changing holiday patterns and the inability of seasonal adjustment to fully reflect these changes.