In an impassioned appeal unprecedented in the last quarter century of leftist politics here, Labor Party leader Neil Kinnock today told his followers that they must jettison the radical left from their movement if Labor is to regain power in Britain.

Ridiculing the "generals of gesture," the "games players" and the militants whose "implausible resolutions" become "pickled into rigid dogma," Kinnock called upon party activists to "understand those realities which, if we ever forget, will damn us."

Kinnock's remark, in a lengthy keynote address to the annual Labor Party conference being held in this southern resort city this week, brought hundreds of cheering delegates to their feet. One parliamentary member said, "Millions of Labor voters have been waiting for 20 years to hear a Labor leader say those things."

Others, a minority, booed and shouted and some angrily stormed off the floor calling the speech "a disgrace." In the lobby outside the conference hall, shoving and shouting matches broke out among delegates.

Some left-wing veterans of the party, formed 80 years ago, dedicated to socialism and paid for largely by the trade union movement, were so astounded by Kinnock's remarks that they would not comment. Militant leader Tony Benn did not even show up for the speech, and Liverpool political leader Eric Heffer left the dais before Kinnock had finished. Later, he sat in a corner and refused to talk to reporters.

For Kinnock, the speech was widely viewed as a make-or-break attempt to demonstrate the leadership ability he often has appeared to lack during two years as party head, and to unify Labor along the only lines that he and many others believe will enable it to win the general elections that must be held by 1988.

"If this movement comes with me," he said, "and I believe with every instinct that the huge majority of this movement wants to, the result will be victory. And victory with our policies and principles intact."

The realities to which Kinnock referred include the most disastrous defeat in party history in the 1983 elections. The two years since have been marked by a series of wounding and lost strikes and increasingly bitter public battles between party radicals and moderates who feel it must broaden its appeal.

As a result, despite widespread and deepening dissatisfaction with the Conservative government of Prime Minister Margaret Thatcher, Labor has been unable to take a strong lead in opinion polls. With its followers sharply divided and its leadership weak, many in Britain's growing middle class -- whose voters Labor needs -- view the party with disdain or fear.

In his speech today, broadcast live nationwide, Kinnock was appealing as much to voters at home, Labor and non-Labor, as to party activists here. To some extent, the biggest threat to Labor comes not from the Conservatives, or Tories, but from the new third force alliance, formed by the traditional Liberal Party and the four-year-old Social Democratic Party. Led by David Owen, a former Labor foreign minister, the Social Democrats were formed by breakaway Labor activists who thought the party was moving too far to the left.

Now running virtually neck and neck with both Labor and the Conservatives in the polls, the alliance threat has both of Britain's traditional parties on the run, and national politics has moved into a campaign phase at least two years before the earliest likely date for the next election. The alliance has shown broad appeal, at least at this early point in the electoral process, to voters who Owen says are tired of the militancy of the left and the stridency and failed policies of the Thatcherite right.

Today, Kinnock referred to the alliance with contempt but reserved some of his most potent ammunition for Thatcher, citing record unemployment, a decline in manufacturing output and a fiscal policy that has driven investment capital out of the country. He promised greatly increased government spending to prime the pump of industry and a campaign to bring British investment back home.

On defense, Kinnock repeated the party's pledge to dismantle Britain's independent nuclear deterrent and to eject U.S. nuclear forces from the country, but he emphasized a commitment to NATO and western defense.

Kinnock's remarks were frequently interrupted by cheers. But it was only in the final 10 minutes of his address, when he referred to splits within the party and faced his internal opponents head-on, that the atmosphere became electric.

Noting that the business of the conference is to adopt resolutions "committing the next Labor government" to action, Kinnock said "there is a precondition . . . that is unavoidable and total. That precondition is that we win a general election, for there is absolutely no other way to put any of those policies into effect."

The only way to help the disadvantaged to which Labor's program is pledged, Kinnock said, "is to get the support of those who are not poor, those who are not unemployed, those who are not victimized."

There is a need, he said, "to recognize completely that we address an electorate which is skeptical. An electorate that is in need of convincing. A British public which wants to know that our idealism is not lunacy, our realism is not timidity, our eagerness is not extremism, our carefulness is not nervousness."

To be successful in a country where union membership is declining and the overall electorate has become more conservative, socialism "must relate to the practical needs and the mental and moral values of the men and women of Britain," Kinnock said. "We must emphasize what we have in common with them. We must not dogmatize and browbeat, we must argue and persuade. That is what people expect. That is what they've got a right to expect, and you know that."

Kinnock directed specific criticism at the city council in Liverpool, dominated by what the party calls "the militant tendency" or "Trotskyite" faction, in a life-and-death battle with the Thatcher government. The city has overspent its budget and refused to limit its spending in accordance with Thatcher's dictums. In a direct challenge to the government in London, and amid promises to workers that such tactics are the only way to victory, the council last week handed out layoff notices to 31,000 city government workers, effective Dec. 31, in the belief that this will enable it to borrow money to tide it over the crisis.

"I'll tell what happens with impossible promises," Kinnock said as Liverpool delegates tried to shout him down. "You start with implausible resolutions, which are then pickled into a rigid dogma and you end with the grotesque chaos of a Labor council -- a Labor council -- hiring taxis to scuttle around a city handing out redundancy notices to its own workers.

"I'm telling you," Kinnock said to cheers from other delegates, "you can't play politics with people's jobs . . . they have no time for such posturing or for the generals of gesture or for the tendency tacticians."

Although a wide majority appeared to agree with Kinnock on the issue of Liverpool, he is likely to run into a less receptive audience Wednesday, when he will debate miners union leader Arthur Scargill. Scargill, a Marxist, is pushing for reimbursement by a future Labor government of all fines levied against the miners during their recent year-long strike.