Battered by record mortgage interest rates, home sales in the Washington area dropped 19 percent in the first 10 months of the year, statistics collected by local real estate boards indicate.

There were 7,000 fewer purchases of single-family houses, town houses, condominiums and cooperatives through October than there were last year, the sales figures show.

District of Columbia sales were hurt the most -- they were off 32 percent -- while Virginia and Maryland home sales were down by 20 to 23 percent.

Brokers unanimously blame high interest rates for the turndown and warn that a recent recovery in sales could be stalled by a second peak in the cost of mortgages.

Mortgage interest rates closely follow increases in the prime interest rate that banks charge their most creditworthy customers and prime has been jumping rapidly recent.

On Wednesday it hit 17 3/4 percent, up 1 1/2 percentage points in the past two weeks, but still short of the 20 percent peak of last April.

Home sales all but dried up after mortgage rates peaked at 17 percent in April, then began picking up in late summer and early fall as rates coasted down to an 11 to 12 percent valley and slowly began to roll back upward.

As a result, October was a pretty good month for the real estate business. In Montgomery and Prince George's County, October sales were ahead of last year and Northern Virginia sales were off only 8 percent. District home sales, however, fell 30 percent behind 1979.

Since the first of October -- when the financing for most of the month's sales was arranged -- mortgage rates have continued to climb. There was 13 percent mortgage money available in early October, but now 14 percent is the lowest rate being quoted by local lenders. Quoted rates range up to 15 1/4 percent for the standard 30-year mortgage with a 20 percent down payment, and go as high as 16 percent for 95 percent mortgages from some lenders.

"The market seems to be fairly strong in spite of the highter interest rates," said a spokesman for the Montgomery County Board of Realtors, "but the full effect of the latest increases hasn't his us yet."

"Obviously when the rates hit these levels it has to effect us," agreed Robert McGrath, president of the Northern Virginia Board of Realtors.

"In our area we're still optimistic," McGrath added. "It looks like our sales in November will be about the same level as October."

During October, agents in the Virginia suburbs sold 1,606 detached houses and apartments, 137 fewer than last year but a decrease of only 8 percent. For the year to date, sales by members of the Northern Virgina group totaled 17,259 units, down 3,950 (22 percent) from the 21,199 houses sold in the same 10-month period of 1979.

Montgomery County sales were up dramatically in October, 47 percent ahead of last year at 771 units, compared with 526 last year. So far in 1980, Montgomery County agents have sold 6,389 homes, 1,885 (23 percent) less than the 8,274 sold in the first 10 months of 1979.

In Prince George's County, October sales totaled 470 units, up by 14 percent (59 houses) from the 411 of last year. Total home sales for the year are 5,328, down from 6,718, a decrease of 1,390 units or 20 percent.

Realtors in the District reported that they sold 55 single-family homes and condominiums last month, down from 72 in October, 1979. Year-to-date totals for the District are 656 units, down 32 percent from last year's 871 units.