LONDON (AP) _ The English National Opera, popular rival of the Royal Opera of Covent Garden, announced Thursday it will stage eight new productions next season in a program of 21 operas.

Despite financial difficulties, the program is a ''firm mixture of the well-known and the unfamiliar, and we are determined to hang on to this at all costs,'' music director Mark Elder told a news conference.

The English National Opera sings all its productions in English and last season played to an average 76 percent capacity at its 2,558-seat Coliseum theater, the largest in London.

The new productions will be Offenbach's ''Orpheus in the Underworld,'' Gounod's ''Faust,'' Mozart's ''Don Giovanni'' and ''The Magic Flute,'' Rossini's ''Moses,'' Wagner's ''Parsifal,'' Busoni's ''Doctor Faust'' and the world premiere of ''The Mask of Orpheus'' by British composer Harrison Birtwistle.

The sets and costumes for ''Orpheus in the Underworld'' will be designed by Gerald Scarfe, a leading satiric cartoonist making his debut in opera.

After 13 years as managing director of the company, Lord Harewood, cousin of Queen Elizabeth II, is handing over the job in June to Peter Jonas, administrative director of the Chicago Symphony Orchestra.

The opera company, which employs more than 600 people, has been given a government grant of just over 6 million pounds ($7.5 million) for the 1985-86 season, 1 million pounds less than it asked for.The sum represents 55 percent of its estimated costs.