Consumer prices in metropolitan Washington during August and September increased at twice the rate of the two previous months, led by sharp increases in the cost of food and clothing.

According to the latest two-month statistics released yesterday by the Labor Department, the local consumer price index rose by 1.8 percent--a figure equal to the entire increase for the four-month period from April through July. That translates to an annual increase of 11 percent.

For the recent two months, Washington's prices increased at the same rate as the national average, 1.8 percent. The cost of living hike here was considerably higher than in Detroit (0.4 percent) or Cincinnati (0.7), but well under that in Portland, Ore. (3.7) or Baltimore (2.7).

Locally, the biggest percentage jump of 6.7 was recorded in apparel prices, particularly women's and girls' clothes, up 12.4 percent. Footwear went up 9.2 percent. These price rises were about double the national average, but the spurt came following a year when Washington area clothing prices were increasing at a slower rate than elsewhere in the country.

The slower annual rise has been attributed by some analysts to heightened competition in this area from new boutiques and discount stores. A Labor Department economist said the spurt in prices during late summer, after an actual decline in June and July, was probably seasonal. The sample of goods surveyed reflected the increase in new fall and winter lines coming into the stores.

"I am aware of about a 10 percent jump in fall merchandise prices over last year," said Larry Hill, general manager of Saks Fifth Avenue in Chevy Chase. "But I can't explain why this region should show a bigger increase than New York" (3 percent).

The 4.1 percent jump in area grocery stores' prices during August and September, however, came as no surprise. Last spring and during early summer, area food prices tumbled during a supermarket price war started by Giant Food Inc., in an effort to boost its share of the regional market. The war was called off when profits dipped precipitously.

As a result, higher prices were recorded during August and September for fish and seafood, soft drinks, fruits and vegetables, pork, eggs, fresh milk and beef as the nation's capital played catch-up with the rest of the country.

Elsewhere, grocery-store food increased by just 0.6 percent during the period. At the same time, the cost of food consumed outside Washington homes declined by 1.4 percent. This may indicate a cut in restaurant prices during the summer doldrums or a cut in dining out due to the state of the economy.

Housing prices increased in this area by a more modest 1.3 percent, compared with the national average of 2.3 percent during the same period. Mortgage interest costs, which rose just 1.1 percent here but 5.1 percent elsewhere, were a big factor in keeping down the housing index despite a marked increase in property taxes. The rise in home-sale prices, 1.1 percent, was comparable to other parts of the country.

High interest rates reduced the sale of existing homes in the Washington area during the first eight months of this year by 41 percent over the banner year of 1978. And the price of the average house sold was stagnant or actually declined when seller subsidies are figured in.

A drop of 1.2 percent in the price of household furnishings was recorded here in late summer, compared with a small increase (0.9 percent) in the rest of the United States.

Another category where the Washington area showed significant variance from the national average was the medical area. Costs here increased by 1.3 percent in August and September, compared with 2.1 percent elsewhere.