Consumer prices shot up a full 1 percent again last month, or 12.6 percent at an annual rate, the government said yesterday. Higher mortgage interest rates were the main culprit; increased housing costs accounted for about three-fifths of the one-month increase.

The figures underscored what economists of all persuasions have been saying: persistently high inflation will be one of the major problems President-elect Ronald Reagan will face when he takes office in January. Further price increases, particularly for food and oil, are already on the way and will be pushing up the inflation rate over the coming months.

The inflation has hit living standards. The purchasing power of an average hour's work fell 0.2 percent in October, the Bureau of Labor Statistics said in another report issued yesterday. Over the past year, average weekly take-home pay has plunged 6 percent after adjustment for inflation.

Food prices in the Washington area rose by 0.7 percent in October, the Labor Department also reported [Article on Page D7].

For the nation as a whole, grocery prices went up 0.8 percent last month, substantially less than the rise in each of the two preceding months. During September grocery prices jumped 1.9 percent, following 2.3 percent in August.

But the relatively good news on food prices is not expected to last. Labor Department economist Patrick Jackman said yesterday that food prices may rise only slowly for a few months "but in the long run, the price expectation is obviously upward."

The Agriculture Department recently forecast that food prices would rise between 10 and 15 percent next year, after the disappearing world grain harvest.

However, while understating the outlook on food, yesterday's price figures probably exaggerate the inflationary impact of higher mortgage interest rates. Most economists agree that the housing component of the consumer price index both overstates and delays the effect of changing interest rates on inflation.

Sharp interest rates rises since the summer have only just shown up in the inflation figures for last month. Home financing costs rose by 3.8 percent in the month, according to the index. House prices were up by 1.5 percent and mortgage interest rates by 1.9 percent, the department said.

Analysts are divided about the likely course of rates in the next few months. Many believe that the 17 percent prime rate now being charged by the major banks to their best customers is the peak, and that rates may come down somewhat in the new year. But the huge increases in the money supply and rapidly rising interest rates so far this fall have taken most economists by surprise.

The consumer price figures give "a very distorted view of inflation during the month of October," said Ben Laden, chief economist for a Baltimore investment firm, T. Rowe Price Associates, "but it is not out of line with the general inflationary environment."

Inflation so far this year has been worse than expected by most economists inside and outside government. In the 10 months through October, prices rose 12.2 percent at an annual rate; in the last 12 months they have risen 12.6 percent.

But price rises for several items in addition to food slowed down last month, according to the consumer price index. Clothing costs rose 0.5 percent in October, compared with a rise of 1.3 percent in September. Transportation was up by 0.8 percent, after a 1.2 percent increase the previous month.

In a separate report, the Commerce Department said yesterday that durable goods orders were up by a seasonally adjusted 1.3 percent last month. The rise followed a jump of 9.9 percent in new factory orders for these goods in September.

New orders for nondefense capital goods, which give a good guide to future spending on plant and equipment, dropped 2.2 percent in October to a seasonally adjusted $20.8 billion. They had risen sharply in September, but not by enough to wipe out a big August fall.

Many economists now believe that the economy may slow down again next year, after the recovery in the second half of 1980. High interest rates could choke off demand for housing and autos. And a large rise in payroll taxes, scheduled for January, could also dampen consumer spending.