Major banks across the country lifted their prime lending rate from 20 percent to a record 21 percent yesterday, and there was no sign that interest rates have peaked.

The sky-high rates are squeezing consumers and businesses alike, and most economic forecasters believe the credit crunch will plunge the nation into recession early in 1981.

"This is a credit crunch, a crisis in the market," declared H. Erich Heinemann, an economist with Morgan Stanley & Co., New York investment bankers. "We are going to have some corporate failures coming out of this."

Chrysler Corp. could be one casualty of high rates, which have depressed new car sales in recent weeks. But many smaller businesses are in the red because of high borrowing costs and less than robust buying by consumers who themselves are being squeezed by inflation.

Many smaller commodity speculators are being hard hit, too, as they find themselves unable to get loans to cover large declines in the value of the contracts they hold for grain, gold and other commodities. At least one speculative commodity fund for small investors, ContiCommodity's McLean Fund 1, was dissolved last week, with both the investors and ContiCommodity suffering losses.

Interest rates have soared because the demand for credit has run head on into the determination of the Federal Reserve to slow the recent rapid growth of the money supply in order to fight inflation. The short-run result likely will be a declining economy in the first half of next year.

"This is the pattern you expect a few months ahead of a recession," economist Beryl Sprinkel of Chicago's Harris Bank said. "Mr. Reagan is inheriting a literal mess."

Heinemann, Sprinkel and a number of other analysts discounted in part reports yesterday from two government agencies indicating continued strength in the economy. The Federal Reserve said that industrial production rose 1.4 percent in November, while the Commerce Department reported that new housing starts in November were running at a seasonally adjusted annual rate of 1,555,000 units, almost as many as in October, which was the highest figure for any month this year.

Most analysts believe output from the nation's factories had not been adjusted last month for a weaker sales outlook. One sign that such a change has begun to take place was a sharp jump in initial claims for unemployment benefits in the last week of November. Similarly, the strength of housing is expected to evaporate as mortgage commitments made earlier are used up. [Details on Page D1.]

Despite the record rates, businesses are still seeking new loans from banks in order to finance expenses such as the cost of keeping goods on retail store shelves or unsold new cars on dealers' lots. Interest rates on such loans regularly are two percentage points or more above the prime, which is the rate banks charge their most credit-worthy corporate customers. Since banks now make most of their short-term business loans with a "floating" interest rate tied to the prime rate, increases in the latter quickly affect most borrowers, not just those currently seeking funds.

More increases in the prime rate could be in store. As of yesterday, when Morgan Guaranty Trust Co. of New York led the move to a 21 percent prime, surpassing last spring's 20 percent peak, major banks were paying effective rates of more than 21 percent for funds they were acquiring from investors on large certificates of deposit. Normally banks try to keep roughly a one-percentage-point margin between the prime lending rate and their highest cost of acquiring funds to lend.

However, short-term rates have gotten so high, market analysts generally expect a peak to come within a few weeks, certainly within a month or two. For one thing, the money supply has been growing less rapidly in the last four weeks, suggesting the Fed will not have to tighten further to achieve its objectives.