Members of the Alexandria City Council last night roundly rejected a request from the city's Taxpayers Alliance that they put a referendum before voters in November calling for property tax cuts and barring the city from enacting any new taxes.

Alliance members who attended last night's council meeting hoping the question would come up left disappointed; the subject was never raised at the public session.

Earlier in the evening the council, meeting in executive (closed) session, had unanimously rejected the idea.

On Monday, Alliance President John Williams sent letters to council members asking them to place a nonbinding "advisory referendum" on the November ballot. Williams cited studies showing that Alexandria residents pay some of the highest taxes in the area.

Voters would be asked to vote yes or no on a resolution that the property tax rate be lowered, that no new taxes be enacted and that the city's borrowing be "stringently curtailed."

"I really don't see the need for so-called advisory referenda. . .when you elect people" to the City Council, Mayor Charles E. Beatley Jr. said after the meeting. ". . .I think all elections are referenda."

Beatley, a Democrat, called the Prince George's County's TRIM amendment, which places a limit on revenues from property taxes and has resulted in service cuts, "a miserable example" of measures that can harm a community.

Republican council member Carlyle C. Ring, considered the alliance's most sympathetic ear on the council, said he was intrigued by the idea of limits on taxes but that a referendum is not the way to accomplish it.

"The real difficulty with referenda is the ability to phrase something that is meaningful," Ring said after the meeting.

Vice Mayor James Moran and council members Lionel Hope and Patricia Ticer, all Democrats, also expressed opposition to the proposal after last night's meeting.

In other action last night, the council:

* Authorized expenditure of $78,961 in city funds to offset cuts in federal and state funding for job training programs in the city.

* Approved commitment of $235,914 in city funds toward new pension plans for seven city police officers and firefighters.

* Received an auditor's report concluding that the Alexandria Redevelopment and Housing Authority, which runs the city's public housing, may face a deficit rising from slightly less than $1 million in 1984 to $2 million in 1988 unless cost-cutting measures are adopted.

* Was told that 19 percent of all property in the city is tax exempt.