U.S. Trade Representative Clayton Yeutter will today impose a limited embargo on steel imports from the European Community as a result of its refusal to ratify a new steel-quota agreement, administration sources said yesterday.

The dispute, which threatens to unravel a U.S.-EC steel-quota pact agreed to earlier this month, revolves around Britain's demand for limits that are high enough so that it can meet the needs of a modern new mill in Tuscaloosa, Ala., for unfinished steel slabs.

Without assurances that it will be allowed to supply the Tuscaloosa plant's slab demand, Britain is refusing to let the EC ratify the new quota agreement.

While the agreement itself doesn't impose quotas on unfinished slab, Yeutter has warned that under it, the United States could unilaterally limit EC exports of that product to 400,000 tons.

The $75 million mini-mill, which rolled its first shipments of high-grade coiled plate -- which is used to build bridges, barges and tanks -- out of its gates yesterday, needs at least 300,000 tons of unfinished steel from Britain to survive next year, according to William Creighton, president of Tuscaloosa Steel Corp.

And, he said, the firm's needs could double by 1989.

"Our very existence as a rolling mill hinges on our being able to get a continuous supply of British steel that we contracted for in 1984," said Creighton.

He added that administration officials gave assurances over the past year that the company would be able to import the needed slabs from Britain.

"We had reason to believe all the way through that we would have the steel supply. We never would have invested $75 million in a plant unless we had very positive assurances the contract would be honored," said Creighton.

It is unclear how firm the assurances were, although company officials said they were given as recently as early this month.

Creighton refused to release a letter that sources said contained the assurances he had received from former U.S. trade representative William E. Brock.

In a press release, the company said only that U.S. officials agreed that its need for British steel "would be taken into account" in the new pact with the EC.

Under the limited embargo taking effect today, all EC steel shipments will be held up at U.S. ports until the Commerce Department certifies they fall within import limits established in a 1982 agreement that expires Dec. 31, officials said.

Shipments that exceed the quotas will not be allowed into the country.

Yeutter acted after Britain balked Tuesday at allowing Common Market ratification of a new steel quota pact that was agreed on early this month by EC and U.S. negotiators.

That pact would extend quotas for another four years, putting the Common Market on a par with other major suppliers of steel to the United States who have agreed to limit their sales under President Reagan's plan to give the domestic industry time to become internationally competitive.

The Tuscaloosa mill is designed to produce coiled steel plates that are now being supplied to the U.S. market by Japan and West Germany.

Its new equipment requires steel slabs made by the continuous-casting method, which Tuscaloosa's owners said is not readily available in the United States.

Before building the new mill, they said U.S. producers had "refused to supply Tuscaloosa's needs for continuous-cast slabs."

As a result, British Steel Corp. agreed to supply the slabs under a seven-year contract.

Once the rolling mill begins to make money, Tuscaloosa Steel said it will build an $85 million electric furnance and continuous caster to supply its own unfinished slabs.

Tuscaloosa officials blamed U.S. Steel Corp. and other large integrated steel companies for pressing Yeutter to limit imports of unfinished steel.

Two years ago, U.S. Steel was blocked by strong labor union pressure from buying unfinished slabs from British Steel Corp. to use in its finishing mills.

The new Tuscaloosa plant, Creighton said, is so heavily automated that it requires few workers and produces high-quality steel at low cost. "What we can do here is make steel very economically because we use very few people," he said.