Giant Food and Safeway have picked up most of the grocery business that was handled by the area's Memco stores before they closed their doors in January, a new study of Washington area supermarket sales shows.

Safeway and Giant both have boosted their local sales by about 15 percent in the last year and both have significantly increased their share of the grocery business.

Giant now rings up about 41 percent of Washington's food dollars and Safeway checks out 32 percent of the local volume, according to the 1983 market study conducted by Food World, a monthly trade publication.

Grand Union, the No. 3 local chain with a little more than 9 percent of the market, and No. 4 A&P, with 3.5 percent of the business, also have substantially increased their sales in the last year.

Grand Union's gains came from opening more of its Basics discount food stores, while the Great Atlantic & Pacific Tea Company's new management and marketing strategies appear to have reversed a long slide in sales, said Food World Editor Jeff Metzger.

Through Best-Met Publications, Metzger and partner Richard Bestany also run a grocery-industry publication in the Philadelphia area. Collecting sales data from food retailers and their suppliers, they compile what is regarded as the best food-market information in the Mid-Atlantic region.

The annual study shows Giant and Safeway each increased their penetration of the Washington market by between 1.5 and 2 percentage points.

Giant's Washington-area sales for 1983 are projected to total $1.33 billion, while Safeway's volume will total $1.03 billion.

The market area includes the District of Columbia and, in Maryland, Montgomery, Prince George's and Charles counties. In Virginia, the market area encompasses Arlington, Fairfax, Loudoun and Prince William counties and the cities of Alexandria, Falls Church and Fairfax.

All four of the big chains are showing sales increases of about 15 percent for the year. The biggest volume gain in the market was posted by Magruder's, the Maryland-based independent that expanded from three stores to five, boosting its volume an estimated 48 percent to $73 million.

Most of the gains for Giant and Safeway have come from increasing sales per store rather than adding additional outlets. Giant has opened two new stores in the last year--including the extraordinarily successful "Gourmet Giant" in McLean--and now has 93 Washington area stores.

Safeway now has 123 stores, three less than a year earlier, but has enlarged some units and replaced others with bigger buildings.

Food World says all of the chains were able to post significant gains by picking up the business that was left up for grabs when Lucky Stores Inc. closed its Memco discount stores with interconnected supermarkets. Bradlees, a Boston-based discounter, plans to reopen Memco later this summer, but without food departments.