BLACKPOOL, ENGLAND, OCT. 9 -- Twelve years after she first addressed a doubting, out-of-power Conservative Party conference as its new leader, Prime Minister Margaret Thatcher stood in triumph before the party faithful today, having restored the Tories to a dominance they believe may last into the next century.

"We are a successful party leading a successful nation," Thatcher told a rapturous audience of party representatives who interrupted her keynote address this afternoon more than 75 times for applause.

"I'm often asked what's the secret," she said. "It's really quite simple. What we have done is to reestablish at the heart of British politics a handful of simple truths." Among them, she said, were a sound budget, the incentive of lower taxes and the promotion of private ownership and free enterprise -- all keystones of her government.

At the same time, Thatcher allowed, her historic third consecutive victory in June also was helped by the continuing disarray and weakness of her opposition.

The four-day Conservative gathering at this northern seaside resort marks the end of this year's conference season, the annual meetings of Britain's political parties that take place each fall. For the main opposition Labor Party, still licking its wounds from the summer's defeat, and the Liberals, embroiled in merger negotiations with the nearly defunct Social Democrats, conference time was a period of soul-searching.

Only the Tories had a reason to celebrate and, as party chairman Norman Tebbit said early in the week when asked if the party was gloating, "I don't mind a little gloat."

Tebbit already has announced his impending resignation to spend more time with his wife, who was crippled in 1984 when the Irish Republican Army bombed a hotel at the Conservative conference in Brighton. Although he is said to have fallen out with Thatcher during the recent campaign, he was clearly a sentimental conference favorite and received a lengthy standing ovation today.

Another favorite of the 4,000 representatives was Cecil Parkinson, a former party chairman who, as Thatcher's new energy secretary, returned to the leadership dais for the first time since he resigned four years ago following revelations of personal misconduct.

But the most fervent adoration was reserved for Thatcher, who entered the conference hall to the orchestral strains of a triumphal campaign hymn written for her by Andrew Lloyd Weber.

Her speech catalogued the government's third-term program, most of it centered on revitalizing Britain's desolate inner cities and on radical domestic reforms in education and local taxing authority that she acknowledged were designed in part to cripple Labor power in local government.

In a brief section on defense, she reiterated her support for a U.S.-Soviet agreement removing intermediate-range nuclear weapons from Europe, which she called "a success for the West, and especially for the United States and for President Reagan."

But, she warned, "reductions in nuclear weapons in Europe have gone far enough" until "massive" Soviet superiority in chemical and conventional forces is addressed. Thatcher does not share West Germany's hope that reductions in short-range nuclear weapons aimed at its territory will be the next subject for East-West negotiations.

In a passing reference to the Persian Gulf, Thatcher described "a time of tension and even danger." Britain, she said, was "giving a strong lead" in helping to keep the international waterway open with its warships and mine sweepers assigned to protect British merchant shipping in the southern gulf.

The Conservatives' conferences generally offer little substantive debate and even less dissent. Unlike Labor and the Liberals, Conservative representatives have no policy-making power and are gathered primarily to endorse policies already agreed upon by the party leadership.

Outside the stage-managed conference proceedings, however, some doubt was raised over the direction in which Thatcher proposes to go in domestic policy. Michael Heseltine, who resigned as Thatcher's defense secretary in January 1986 and is seen as a contender for the post-Thatcher party leadership, criticized her dependence on private investment for the inner cities program, and her refusal to spend more public money.

Others have questioned the four-part program known inside the government as the Great Education Reform Bill, or "Gerbil." It includes imposition of a standardized "core curriculum" and nationwide achievement tests. Under the new system, individual state schools also will be able to "opt out" of control by mostly Labor-dominated school boards. Thatcher said today the boards teach "antiracist mathematics" and "the inalienable right to be gay," rather than how to count, multiply and respect "traditional moral values."

Schools that opt out would be administered by local parents and teachers, would be able to select their own students, could decide to receive central government grants and could draw up their own individual budgets without local government interference.

Another key reform is the replacement of property taxes with a "community charge" levied equally on all adults in a jurisdiction. Commercial tax rates would be assessed separately by the central, rather than local, government.

Thatcher has described this system as more fair, in that it does not discriminate against property owners -- many of whom are more likely to vote Tory than the 25 percent of Britons who still rent public housing from local government councils -- and will promote inner city investment by lowering business tax rates.

Although the new tax system has been harshly critized by some Conservative members of Parliament, it was roundly approved by conference representatives.

Equally lauded were nonspecific promises by John Moore, Thatcher's new social services secretary and another post-Thatcher leadership aspirant, to turn over some segments of the National Health Service to private contractors.

The only major disagreement from the floor came when Home Secretary Douglas Hurd reiterated his opposition to reinstating hanging. An emotional issue at Tory conferences since it was abolished in 1969, capital punishment is advocated by a majority of Britons, including Thatcher.