A House subcommittee last week slashed to zero funds for National Children's Island, an innovative recreational and educational park to be built by the District of Columbia on two small islands in the Anacostia River. The city had earmarked $193,800 for the park in next year's budget.

The subcommittee would also end a bureaucratic struggle over control of the project by placing it under the District's Recreation Department. However, it did not give the Department any funds for Children's Island.

The move to the Recreation Department would appear to end control of Children's Island by its present executive director, Joseph C. Henson.

The project has been in trouble for months, and has been questioned by city officials. It was started in early 1975 by the D.C. Bicentennial Program office. Completion is already a year behind the target date of July 4, 1976, and estimated costs have risen from $3 million to $5.7 million. In addition, Children's Island has been operating virtually without city oversight since the Bicentennial Program office closed last year, according to a city government source.

The orginal plan provides for special facilities for the handicapped, a children's theater, library and museum, an international mall with rotating exhibits and demonstrations, an animal petting center, a windmill, greenhouse, nature sanctuary, ranger tower and a carrousel.

The action last week by the House District Appropriations subcommittee undercut a proposed meeting of city officials to discuss Children's Island. The meeting, orginally scheduled for the end of June, was delayed while District employees put the finishing touches on the city's budget. Also, a report by Henson defending the project was not completed until this week.

Recreation Department officials expressed dismay at being saddled with a $5.7 million project with no city financial support. They said it would take time to assess the effect of the move. Frances Green, the department's budget officer, said the department would protest and appeal if the subcommittee's action is ratified by the full House Appropriations Committee and by the House itself.

Earl C. Silsby, the subcommittee's staff director, said he expects both the House and Senate to ratify the move.

"The fight is not going to be over Children's Island. The fight is going to be over the Advisory Neighborhood Commissions," he said. The subcommittee, chaired by William H. Natcher (D-Ky.) also eliminated $1 million for the 36 citizens' groups last week.

Joseph C. Henson's assessment of the Children's Island action was gloomy. He said Children's Island would lose its status as a tax-exempt, nonProfit corporation, and would be ineligible to receive private and federal grants.Such grants have been a major source of funding for the project. Earlier in the year Henson said that if the project went to one of the city's line departments, it would never be built.