Britain and Argentina are sending warships to the disputed Falkland Islands after their long-simmering feud over control of the sparsely populated territory erupted earlier this month into what the foreign ministers of both countries have described as a serious confrontation.

Without detailing the British naval force being sent to the islands, in the southern Atlantic off the tip of South America, Defense Secretary John Nott said today it would be adequate to defend British interests.

Nott said Britain still seeks a diplomatic solution but other officials said the crisis is being taken very seriously here. The confrontation has been called "potentially dangerous" by Britain's foreign secretary, Lord Carrington, and "grave and serious" by Argentine Foreign Minister Nicanor Costa Mendez.

Britain reportedly has ordered a nuclear-powered submarine and other vessels to join a Royal Navy ice patrol ship facing several Argentine warships in the vicinity of the Falklands. Argentina also is reportedly sending its only aircraft carrier. British destroyers and frigates in the Caribbean and at Gibraltar have been put on alert.

The current troubles began 11 days ago when a group of Argentine scrap metal dealers landed on remote South Georgia island, 800 miles east of the rest of the Falklands to dismantle an unused whaling station.

The Argentinians had a contract with the British owner of the whaling station and notified British officials in the Falklands of their intentions. But because they did not obtain advance immigration clearance and raised an Argentine flag after landing, according to the British, they were asked to leave.

All but 12 of the original 50 left, according to British officials and representatives here of the 1,800 residents of the Falklands, which have been occupied continuously by British settlers and their descendants since 1833.

The Argentine Foreign Ministry said Britain has no right to order the men off what it considers Argentine territory. Citing a brief occupation of the islands by Spain during the 18th century, Argentina has long claimed sovereignty over the Falklands, which they call the Malvinas.

The British ice-patrol ship Endurance, with some of the 36 Marines normally stationed in the Falklands, was sent to the whaling station to back up the British demand that the rest of the Argentinians leave.

Argentina responded with three warships and was reported yesterday to be sending more. Although British officials refuse to comment, it has been made known here that at least one British submarine capable of sinking surface warships is on its way to the Falklands, to be followed if necessary by large surface warships.

Prime Minister Margaret Thatcher's government has been accused by members of Parliament here of responding slowly to Argentina's military moves and crippling British preparedness for such emergencies by reducing the Navy's surface fleet.

Carrington said yesterday that intensive secret negotiations with Argentina had so far failed to resolve the dispute.

U.N.-sponsored negotiations begun in 1965 have made slow progress on competing British and Argentine claims, although agreements have been reached on trade, communications, educational and medical facilities and customs regulations for Falkland island residents.

Britain and Argentina have otherwise enjoyed close trade and other ties in the past. One of the Argentine destroyers deployed for the current confrontation is British-made and the Argentine aircraft carrier was bought from the British Navy.