BRITAIN'S PRIME MINISTER, James Callaghan, has set off a splended row in London by appointing his son-in-law to be ambassador to Washington. Temperature are running particularly high within the Prime Minister's own Labor Party. Beneath the furious charges of nepotism there is doubtless another and more substantial issue. The ambassador-designate, Peter Jay, has been for 10 years the economics columnist of the London Times, and his view of the world has not been terribly flattering to the socialist verities that the Labor Party cherishes. The charge of nepotism appears, in fact, to be a bum rap. The choice of Mr.Jay evidently owes more to his old friend David Owen, the new foreign minister. But the incident brings up a perennial question: What's an ambassador for?

The British government is very much on the defensive in this affair, emitting a susurration of unattributted explanation tht strikes us as inane. There was the anonymous suggestion that perhaps the incumbent ambassador, Sir Peter Ramsbotham, was too irrvocably middle-aged to deal with the bright young people who swarm around President Carter at the White House. (Sir Peter is 57. Mr. Jay is 40. Mr. Carter is 52. Secretary of State Vance is 60. AMy is 9. So what?) Then there was the hint that the embassy had been inviting the wrong people to its parties - these affairs are said to be either too stiff or, according to an alternative rumor, too frivolous for a country in such economic trouble. It's the sort of stuff that governments put around when they're embarrassed.

Governments have their own reasons for moving diplomats, and ambassadors of all ages are welcome in this capital. Americans are a broad-minded people, who also will not hold family associations, or previous newspaper connections, against a foreign visitor. But there is no pleasure in seeing Sir Peter leave. He has ably represented his government here, working with notable grace and skill at a disheartening time, when the main business between the two countries was a series of divisive crises of economic polity and finance.His successor will arrive at a happier moment, as North Sea oil begins to balance Britain's international accounts, strengthen the pound and lift the spirits of British diplomacy.