After agonizing for months over the plunging pound, the British government is now worrying over a new and unforseen problem: the fast-rising pound.

Persons at the highest levels of government here fear that if the newly robust currency keeps gaining, British will breach its pact with the International Monetary Fund to "maintain" competitive export prices.

But if the authorities step into halt the ascent, Britain will violate another pledge - this one was made to the Basle creditors to run down foreign deposits of sterling here.

"We are in a cleft stick," one key aide to British Prime Minister James Callaghan had said to the dilemma. The fact is that British has made mutually inconsistent promises.

This in part lies behind last week's disclosure from 10 Downing Street that Callaghan will now keep a close personal watch on Britain's economy in general and the pound in particular.

The one silver lining is that the promises were really made to the same creditors. The International Monetary Fund, which is lending Britain $4.9 billion, gets most of this sum from the U.S., Germany and Japan. The Basle credit of $3 billion is largely coming form the identical trio.

So Callaghan and his team can hope for some understanding. Indeed, they regard the new U.S. Treasury Secretary-designate, W.Michael Blumenthal, as considerably more sophisticated and flexible than his predecessor, William Simon.

The problem was created by these circumstances: From March 2 to Oct. 28 last year, the pound fell a dizzying 23 per cent, from $2.02 to $1.555. That was supposed to make British exports cheaper, stop the drop and lead the economy out of stagnation. To prop up the pound and stop it from shrinking further and upsetting currency markets everywhere, the IMF gave Britain the $3.9 billion loan.

To get it, Denis Healey, Chancellor of the Exchequer, gave the IMF a 12 page letter full of promises. One said Britain will "maintain stability in the exchange markets consistent with the continued maintenance of the competitive position of UK manufacturers both at home and overseas."

The government regards this as a firm undertaking to stop a rising pound from wiping out the competitive price advantage that exporters supposedly gained from the falling currency.

Since Oct. 28, the rise has been almost as spectacular, 10 per cent in less than three months to $1.71. The pound bounded back for two reasons: One was the $7 billion raised from the IMF and in Basle. The other was a belated appreciation by the multinationals and banks - the big currency traders - that North Sea oil will transform Britain's foreign accounts dramatically this year. Instead of seeking foreign currencies to pay bills abroad, Britain is expected to show a payments balance at the end of this year or early next year. The foreigners will be seeking pounds to pay their bills.

This sharp change in sentiment "threatens" to drive the pound still higher. The government could honor its MF pledge by stepping in to sell pounds for marks dollars and the rest. That would hold the pound's exchange rate down. But it also would mean that foreign holdings of sterling in Britain would increase.

This, however, is exactly what the Basle agreement and its $3 billion credit are supposed to stop. Britain at long last has persuaded itself that foreign sterling deposits cost more than they are worth, that sudden withdrawals by foreign sterling holders always worsens any fall in the pound.

So, as Healey said last week, the new Basle pact aims at enabling Britain "to achieve an orderly reduction in the role of sterling as a reserve currency." In plainer English, get rid of foreigners' sterling balances.

The government has no answer and cannot have an answer tothe mutually inconsistent promises it has made. However, outside experts are saying that the government should let nature takes its course, that if the pound rises, the benefits are greater than the costs, that the IMF pledge must be weakened.

The logic here is that Britain simply did not gain the expected competitive edge from a falling pound. British exporters, with little competion among themselves, did not cut their prices in marks or francs as the pound cheapened. They kept them more or less where they were and pocketed the windfall exchange profits.

New data published here show this has been the case. From the first to the four quarter last year, the pound fell by more than 20 per cent. But Britain's exporters picked up only a 4 per cent increase in competitive price advantage over rivals in the U.S. Germany, Japan, Italy and France.