An impressive Terrace Theater recital yesterday afternoon made abundantly clear the reasons for the rapid rise of Britain's Endellion String Quartet. Playing with rare elegance and refinement, the ensemble projected an urbanity seldom heard in any kind of performance these days. The group seemed, above all, eminently civilized, the reflection of a tradition that can be traced back at least to Elizabethan days.

Founded only three years ago, the ensemble won several prizes in its own country and then hopped across the Atlantic last year to win the Young Concert Artists International Auditions in New York. As a result of that win the quartet made its American debut yesterday by opening this year's Young Concert Artist Series at the Kennedy Center. Tomorrow the group will perform in the same series at New York's 92nd Street Y.

The chemistry of a successful string quartet mix always possesses a certain mystery. The members of the Endellion come across like figures out of an English classic, with first violinist Andrew Watkinson the eloquent hero, second violinist Louise Williams the lyrical maiden, violist Garfield Jackson the able aide and cellist David Waterman the courtly wit. As the opening Haydn Quartet, Op. 20, No.4 demonstrated, they are all capable of the most polished and sharp-edged repartee.

Britten's Third Quartet, a highly personal statement, further revealed the ensemble's precision and unity of style along with its expressive sensitivity. The closing Beethoven Quartet, Op. 74 in E-flat major, was marked by an exceptional attention to detail in a finely shaded interpretation.