The D.C. City Council's Human Resources Committee approved legislation yesterday that would permit welfare recipients to choose among a number of funeral homes for city-financed services, ending a monopoly now enjoyed by one large firm.

Under the measure, as amended by the committee, the city would compile a list of approved furneral homes which - at the outset - would be paid $750 by the city for each funeral service, including burial plot.

The payment would rise in future years at the same rate as the federal Consumer Price Index.

Action by the committee sent the measure to the full City Council, which may give it preliminary consideration July 31. If enacted, the meausure would go into effect Jan. 1 when the contract for the present arrangement expires.

If approved, the measure would end a system under which the D.C. Human Resources Department makes a contract based on a standard per burial price with one funeral director, who then handles the funerals for all city welfare recipients.

The current contractor is the W.W. Chambers Co., a white-owned firm that in fiscal 1978 handled 480 contract burials.Its current basic fee is $585 for an adult burial, with somewhat lower rates for children.

Black undertakers propsed an end to the contract system and the substitution of the method proposed in the new council bill, which would give a direct grant to survivors to choose their own undertaker.

The bill was introduced by Council Members Nadine P. Winter (D-Ward 6) and David A. Clarke (D-Ward 1). It was approved yesterday by a 2-to-0 vote of the committee, with John L. Ray (D-At Large) and Wilhelmina J. Rolark (D-Ward 8) supporting it. Polly Shackleton (D-Ward 3), the committee chairman, and Charlene Drew Jarvis (D-Ward 4), whose husband is a funeral director, both abstained.

As recommended, the city grant would pay the full cost of a funeral. Friends and relatives could contribute up to $40 extra for the cost of flowers and newspaper death notices.