Prices in the Washington metropolitan area rose by 1.4 percent in October and November, three times the national average, the government reported yesterday.

But the Labor Department also said that for the 12 months ending in November, the rate of inflation was 8.6 percent here, slightly less than the nationwide rate of 9.6 percent and the same as the rate for the Baltimore area. The figure also is lower than those reported for Philadelphia, New York and Boston, the three other major East Coast metropolitan areas that the government studies for price data.

The government figures, complied by the Bureau of Labor Statistics, in essence are the final local inflation figures for 1981 because the information is tabulated every two months for regions the size of the Washington metropolitan area.

The inflation rate for the 12 months is well below the 10 1/2 percent rate reported in this area for the same period last year and the 12 1/2 percent figure for 1979, demonstrating the easing of inflation here predicted by local economists.

Increases in the cost of home ownership, food and transportation were the primary factors behind the sharp 1.4 percent increase for the two-month period, although grocery costs rose only 0.6 percent due to increased retail competition in the area. That figure compares with 4.1 percent for the previous 60 days.

The government, which compiles monthly food price information, said that in November grocery store prices rose by 0.1 percent compared with 0.5 percent in October. The costs of fruits and vegetables dropped by 2.8 percent after having risen by 2.2 percent for the earlier period.

For the year, the costs of meats, poultry, fish and eggs here dropped by 4.1 percent compared with a nationwide rise of 0.3 percent. But prices rose by 8 percent for cereal and baked goods compared with a nationwide rate of only 4.2 percent.

The cost of restaurant eating actually remained unchanged for the two months and rose by only 1.9 percent for the year compared with a nationwide rise of 8 percent.

But the costs of either owning or renting a home here rose sharply, the government said. The costs of renting a home rose by 3.4 percent over the period, while the home ownership index, fueled by higher mortgage costs, rose 3.6 percent, three times the figure for August and September.

The overall cost of housing rose by 11.1 percent here for the year compared with a nationwide figure of 11.9 percent. That gap, however, is attributed to the cost of of fuel and other utilities, which rose by 9.6 percent here compared with 15.4 percent nationwide.

But the costs of renting rose by 11 1/2 percent over the year compared with a nationwide rate of 8.4 percent. The costs of owning a home rose by 14.9 percent over the 12 months compared with 11 1/2 percent last year.