Eight soldiers were killed and 49 other persons injured today when bombs claimed to have been placed by Irish nationalist terrorists exploded at two London locations where British ceremonial military units are watched daily by tourists and other civilians.

A Scotland Yard spokesman refused to speculate whether the blasts signaled the start of another round of terror by members of the Provisional wing of the Irish Republican Army--which claimed responsibility for today's attacks--saying "it is far too early" to judge. Assistant Chief Commissioner Gilbert Kelland warned, however, that "this threat from terrorists is always with us," and he cautioned that "everyone in Britain must be on the alert from now on."

Today's explosions were the first such incidents since last fall, when a series of blasts over five weeks killed three persons and wounded nearly 40.

The first bomb today went off just before 11 a.m. (6 a.m. EDT) as a detachment of scarlet-coated troopers from Queen Elizabeth's Household Cavalry rode through Hyde Park on their way to the changing of the guard at the Horse Guards military parade ground in Whitehall, site of many government offices, and of a popular pageant for London visitors. An explosion that may have been triggered by remote control blew up a pale-blue car and unleashed a torrent of four- to six-inch nails enclosed inside a plastic bomb.

Two soldiers of the Household Cavalry were killed, and 21 persons injured, including 4 soldiers and 17 civilians. Eight horses were either killed or destroyed on the spot.

Two hours later a bomb exploded under a bandstand in Regent's Park where a band of the Royal Green Jackets was entertaining a lunch-time crowd, mainly children and retired persons. Six Army bandsmen were killed and at least 28 people were injured, including 24 soldiers and 4 civilians.

The band was on a visit to London from its normal station in Northern Ireland. Members of the band are noncombatants whose wartime job would be to work as stretcher-bearers.

The carnage and the noise of ambulances, police vehicles and helicopters gave parts of central London on this sunny summer day the quality of a city under siege. A number of streets where other bombs were suspected were closed off for hours and police with megaphones ordered office workers to stay inside, open their windows and draw their curtains.

Both explosions could be clearly heard some distance away. Prime Minister Margaret Thatcher learned of the first as she went to a Cabinet meeting. Aides said there was no doubt at Downing Street, about a mile from the Hyde Park scene, that a bomb had gone off somewhere. Later in Parliament, Thatcher condemned the IRA terrorists as "evil and brutal men" and she called the attacks "callous and cowardly."

It was not clear tonight why the Provisional IRA, which is fighting to drive the British out of Northern Ireland and to unite the province with the Irish Republic to the south, had chosen this moment to mount so bloody an assault in London. A statement released in Dublin and Belfast invoked Britain's recent victory over invading Argentine forces in the Falkland Islands, declaring, "The Irish people have sovereign and national rights which no task or occupational force can put down . . . Now it is our turn to properly invoke Article 51 of the U.N. statute and properly quote all Thatcher's fine phrases on the right to self-determination of a people."

The government's minister for Northern Ireland, James Prior, is currently in Washington to urge restraints on private American funding for the IRA, to explain a new plan for local self-administration in the province and to encourage American investment there.

After meeting Tuesday with Deputy Secretary of State Walter Stoessel on the subject of Northern Ireland, Prior said, "I want to make it perfectly clear to the terrorists and everyone else that we don't intend to be deflected because of attacks in London and anywhere else," Reuter reported.

The bombs may have been connected with the conviction in Ireland last week of Gerard Tuite, a notorious IRA guerrilla who fled to Ireland and was charged there under a 1976 law aimed at prosecuting terrorist offenses committed in Britain. In addition, five IRA suspects reportedly were arrested in the republic over the weekend in connection with a major arms find in Donegal County, on the western border with Ulster.

In Dublin, Prime Minister Charles Haughey condemned the "callous and brutal murders" and the damage they did to "the good name of Ireland and the cause of Irish unity."

Ireland's refusal to support sanctions against Argentina during the Falklands conflict severely strained its relations with Britain. After months of being preoccupied with other matters, today's devastation is a reminder for British officials, in particular, of the serious problem they face in Ulster and the role the Irish government might play in easing the trouble.

The two bombings were clearly intended to wreak the maximum damage to military units engaged in purely ceremonial functions and to those who come to watch them. Both sites are well known as part of the London that draws millions of visitors each year.

This is especially the case with Hyde Park Corner, at the heart of the city, opposite the rear of Buckingham Palace gardens and across from the Wellington Museum. The barracks of the Household Cavalry is on Rotten Row, the roadway that runs along the southern side of Hyde Park, parallel to the shopping and business area at Knightsbridge.

As the mounted troopers reached a point a few hundred feet from the intersection, the car bomb went off. The horses took much of the brunt of the blast. Eyewitnesses described in grisly detail the scene of severed human limbs and ravaged animals.

The scene at Regent's Park was as bad. The band was playing selections from the musical "Oliver" when the explosion went off. Onlookers rushed to the aid of the injured with towels and other primitive first aid devices while police rushed to the scene.

The wounded were taken to three London hospitals, where health workers were in the second day of a three-day strike for higher pay. Union leaders ordered them to return to work immediately so the wounded could receive proper treatment.

Tonight, police were engaged in a major new search for IRA weapons and supporters. Last fall's terrorist attacks eventually involved 16,000 police officers and led to 111 arrests. But a suspected cache of explosives was never found.