The Alexandria City Council voted last night to spend an additional $53,000 to shelter the homeless this winter, but officials said the city's homeless population is growing so fast that services will still have to be cut.

On unanimous votes, council members gave $25,000 to a church that is opening a shelter for 30 homeless men and earmarked an additional $28,000 to expand a program that temporarily houses people in a hotel. These expenditures, together with existing programs, will bring the city's total spending on the homeless this year to $166,000.

Despite the increases, City Manager Vola Lawson said some homeless people still will have no place to sleep. "We expect to turn people away to stay within the . . . budget," Lawson said in a memo to council members.

Because of increasing demand, Lawson said the city will allow single people to stay in subsidized hotel rooms no more than four consecutive nights, a decrease from the current five-night limit. Homeless families will be allowed to stay longer.

And no homeless person will be allowed to use the city program more than once a year. Until now, anyone has been able to use the program every six months.

Without the additional city aid, prospects for the homeless had looked even grimmer. Last winter, two Alexandria churches sponsored shelters, but one of those churches decided not to reopen its facility this year.

The city failed this year in an effort to build a 65-bed shelter for the homeless near Eisenhower Avenue. Officials had hoped to place modular housing units on land owned by Metro, but legal restrictions on the land blocked the project.

The expenditures approved last night will allow Meade Memorial Episcopal Church to open a 30-bed shelter for homeless men, replacing the facility that will not reopen. The city also will be able to expand its motel temporary-housing program slightly.

The only other facility for the homeless in the city is operated by Blessed Sacrament Catholic Church and does not receive city funds.

Council member T. Michael Jackson praised local churches for confronting the problem of homelessness and pledged that the city would open its own shelter before next winter. "With the help of people like you," Jackson told shelter organizers, "we can meet a serious social need."

While there are no exact figures on the number of homeless people in Alexandria, Lawson said the city sheltered an average of 188 persons a month during July, August and September. That number is expected to rise as the weather becomes colder.