British government today yielded to the law of supply and demand its currency to make a big leap upward.

By the end of the trading day here, the pound had gained an impressive 6.3 cents to $1.84. This is a climb of 3.5 per cent and the end is not in sight. Against all major currencies, the pound expanded 3.4 per cent on the day.

At one point in the feverish trading, sterling touched $1.843, but the Bank of England stepped in, as it has been doing for months, buying up foreign currencies to push the pound back down.

The government thus made clear it is not allowing a free float, letting market forces along determine the currency's exchange value. It is instead engaging in a more relaxed version of a "dirty" or controlled float.

In the eyes of some experts here and the U.S. Treasury, the move is overdue. The government has been holding down the pound's rate deliberately as a device to protect. British manufacturers from imports and to provide a hidden subsidy for their exports. This makes manufacturers happy but it is an expensive game for consumers.

Now, because of the costlier pound, Britain should take in more cheaper goods from abroad and find it less easy to sell the more expensive British products in all overseas markets.

The Treasury, which determines Bank of England policy, gave a technical reason for the move. It noted that the policy of holding the pound down meant that huge amounts of marks, francs, dollars and other currencies may now be as high as $36 billion.

This inflow must result either in an increase in the money supply or it must be mopped up by selling bonds. The first course would but pressure on prices in an economy wrestling to reduce an inflation of 14 per cent. The second, increasing borrowing, would force up interest rates and choke off investment in new plant and other forms of demand.

Something had to give, and the government decided it should be the price of pounds abroad.

No one know how high the pound will go, but there is every reason to think that it will be a "hard" currency, one for whcih demande exceeds supply, for the next 10 years or so.

This judgement would have astounded most observers a year ago when the government was desperately trying to stop the pound from slipping below $1.56. It was obvious even then, however, that North Sea oil would drastically transform the pound's prospects.

Instead of paying out several billion dollars for imported oil, Britain is already taking half its domestic needs from its own waters. It will become an oil exported by 1980. The Treasury estimates that oil will addd no less than $29 billion to Britain's balance of payments in 1985 alone.

It is almost inconceivable that this surplus could be wiped out by any deficit in trade. Yet, it is this fear that partly accounts for the recnt policy of holding the pound down to spur exports and curb imports.

To be sure, a return of raging inflation here would reduce the oil bonus. Skyhigh prices would cripple British sales overseas and open the door to large import flows.

The rising pound itself will help hold down inflation, however, and provide extra relief to consumers. About one-forth of Britain's total output is imported. These good - food, raw materials for industry and the rest - are now cheaper. It takes fewer and fewer pounds to buy more and more goods priced in dollars or yen. Each 4 per cent rise in a sterling slices about 1 per cent off the cost of living. So the higher the pound goes, the more inflation retreats.

There is even a multiplyer, effect. One immediate cause of Britain's inflation is increased wage demands. As the inflation rate tapers off because of the rising pound, workers are likely to press for smaller pay gains.

The British "losers" in all this ara the exporters. So the Confederation of British Industry, spokesman for big business, said that the pound's rise "will not be welcome to industry."

An undervalued pound in effect subsidizes their foreign sales and creates a tariff-like wall against foreign competition, all at the consumer's expense.

In West Germany and Japan, where industrialists dominate policy, this technique of artifically suppressing the value of the currency, has been employed for years. It accounts in part for the huge trade surpluses both enjoy.

Some of this is now being reversed a little. That is why the dollar is falling and mark and yen are rising. In effect, the currency changes are stripping some of their subsidy and protection from West German and Japanese industrialists.

With its free trading tradition, it is harder for Britain to employ these techiniques over a long period. The cartel spirit, however, is much more alive in West Germany and Japan, so their manufacturers persuade their governments to resist the free play of supply and demand and keep their currencies undervalued.

Those unversed in finance invariably describe the West German and Japanese purchases of foreign currencies as "support for the dollar" or "propping up the pound." They do not understand that the "support" and the "propping" are for West German and Japanese manufacturers, and little different from the imposition of a tariff.