The Falls Church City Council has approved a $10.8 million budget for the fiscal year beginning July 1.

In approving the fiscal 1981 budget, which is 7.5 percent higher than this year's, the council last week voted to lower the property tax rate by 8 cents, to $1.11 for each $100 of assessed value. That rate is the lowest in Northern Virginia, one cent lower than in Arlington County.

"At a time when the rate of inflation in the metropolitan Washington area is running between 18 and 20 percent a year, it is encouraging that the council has been able to limit the tax burden on Falls Church residents," said Mayor Harold L. Miller.

Despite the reduced tax rate, city officials say most Falls Church residents will face in increase in their tax bills because of a rise in biennial property assessments. The average single, detached home in Falls Church which was valued at $69,200 two years ago is currently assessed at $85,200. Because of that rise, the tax bill for the average homeowner will rise by 14.8 percent.

Almost half of the Falls Church budget, $4.7 million, is earmarked for the city schools. While Falls Church contracts with Fairfax County for many of its services, such as solid waste disposal and social welfare programs, the city continues to maintain its own school system.

"I think schools are the paramount importance in the city of Falls Church," council Vice Chairman Carol DeLong said in an interview this week. "I wish we could do it with less expenditures from the city, but lacking in state and federal support, we probably are going to have to carry the ball by and large by ourselves."

The council also approved $556,000 for its share of the Metro operating deficit. That represented $115,000 more than the city's current share of Metro costs.

The current personal property tax rate of $5.50 for each $100 of assessed property value will remain the same next year. But charges for water and sewage will rise.

The sewer rate will increase from $8.40 for the first 10,000 gallons of water to $12. The water rate increase, from $9 to $9.40 for the first 10,000 gallons, will affect more Fairfax County residents than those in the city. Falls Church, which is only two miles square, provides water to residents in a 31-square-mile area.