Energy prices fell last month, food prices were level and inflation slipped to the lowest level in nine months, the Labor Department reported yesterday.

The consumer price index rose at a seasonally adjusted rate of 0.4 percent -- in annual terms about a 5 percent inflation rate, the department said.

Even so, prices rose faster than wages; the pruchasing power of an average hour's work fell 0.1 percent for the month and was 0.6 percent less than a year ago, the department reported.

Gasoline prices, which had risen 13.2 percent in the first quarter after the president removed price controls from oil, dropped 1.4 percent in April and an index of consumer prices for food and beverages remained unchanged.

But economists warned that likely future food price increases and rising mortgage rates may push the consumer price index up again.

And a spokesman for the president's Council of Economic Advisers, even while saying the April figures were encouraging, cautioned against reading too much into any one month's or quarter's results. "If you take out the traditionally volatile elements in the consumer price index, such as energy, food and housing, the underlying rate of inflation is still pretty close to 10 percent," he said.

Treasury Secretary Donald T. Regan, however, said the April figures are a sign that "things are cooling down." The administration expects the economy to shift into a slower gear over the next six months or so, and thinks that this will help bring down interest rates and inflation generally.

But even as the new inflation figures were released yesterday, major banks in New York were raising their prime lending rates, the interest rates on which most business loans are based, from 20 percent to 20.5 percent reflecting increases in short-term rates in money markets. It was the sixth increase in the prime since mid-April and the second this week and brought the key rate to within a percentage point of its record high of 21.5 percent registered last December.

In another development, the nation's money supply measure known as M1-B fell to an average of $428.8 billion for the week ended May 13 from a revised $431 billion the previous week. M1-B is the measure which includes currency in circulation and checking deposits in financial institutions. The larger than expected decline reflected the Federal Reserve Board's policy of restricting growth in the money supply which has been reflected in rising rates for short-term loans.

William E. Sullivan Jr., a senior vice president at Bank of New York, said that the money supply report may indicate that some of the pressures that led to the most recent increase in the prime were artificial and that the rate may hover where it is until further signals come from the Fed.

The news of a decline in the inflation rate came at a time when President Reagan is attempting to sell a package of tax proposals that opponents have charged will trigger a new round of inflation.

The 0.4 percent increase in the CPI for April followed increases of 0.6 percent in March and 1 percent in February. The index itself rose to 265.1, meaing goods that cost $100 in 1967 cost $265.10 last month.

"I think it's obviously very good news. It's going to help consumer spending," said Sandra Shaber, a senior economist and director of consumer market services for Chase Econometrics, referring to the one-month figure.

Both the possibility of rising food prices and mortgate interest rates remaining highe "provice further basis for caution in not reading too much into one month's numbers," said the Council of Economic Advisers spokesman.