Fifty-five Loudoun County families will receive notices this week that their state-provided day care subsidies will be cut off as of Sept. 30, according to Joan Linhardt, director of the county's social services department, which administers the funds.

Demand for the subsidies, which the Virginia General Assembly established in 1986 to help parents, particularly single mothers, stay off welfare, is so great that in some jurisdictions the money is expected to run out by the end of this month unless emergency funds are found.

Linhardt and other social service officials have predicted that without the subsidy many parents will be forced to quit their jobs and receive welfare.

The state initially appropriated $3 million for the program, with the money equally divided between fiscal 1987 and 1988. Although demand was limited in the early going, by the end of July the program was serving 780 families statewide, and spending at the rate of $200,000 a month, according to state officials.

A request for an additional $1.5 million for this fiscal year, which began July 1, is reportedly on Gov. Gerald L. Baliles' desk.

Fairfax and Arlington counties and Alexandria do not anticipate having to drop families from their programs.