John Adams has an extraordinary following in this country, the kind any composer would envy. Last night he drew a solid audience to the Albert Hall for the world premiere of his Doctor Atomic Symphony. This four movement, 42-minute work is an orchestral digest of his latest opera, already staged in San Francisco but not due in London until English National Opera performs it in 2009.

The opera's subject, to a libretto by Peter Sellars, is the making of the first atomic bomb, detonated in the Mexican desert in 1945. The symphony uses orchestral passages from the score with new linking music. A vivid account by the BBC Symphony Orchestra, conducted by Adams, whetted one's appetite for the opera proper but also proved effective as a stand-alone piece.

The opening movement, Laboratory, launches explosively with surging brass, motoric strings and thunderous percussion.

Urgent, throbbing, industrial music ebbs and flows before moving, without a break, to the second section, Bedroom. The poetry-loving scientist J Robert Oppenheimer, the central character, is in bed with his wife. A gorgeous wash of sensuous music, with a tender cello theme, depicts Oppenheimer - finally dragged away from his statistics and data - reading erotic Baudelaire to her as an expression of love.

Back in the lab, panic is rising in the third movement, as the team of scientists prepare for the test explosion. Haunting chromatic brass lurches into robotic chaos. Only in the final movement, Trinity, can we imagine how the vocal writing might sound. Oppenheimer's last, soul-searching aria sets an anguished devotional poem by John Donne ("Batter my heart").

An eloquent trumpet solo, at once noble and elegiac, leaves its plaintive melodic mark in this most expressive finale.

The all-American Prom also included Adams's popular Century Rolls, a spiky, jazz-inspired challenge to our "machine age" with Olli Mustonen as the exuberant and virtuosic piano soloist.

The concert opened with Copland's Billy the Kid suite in a performance rich with Grand Prairie hoedown swagger and mordant tunefulness. Here, as in the entire evening, the timpanist held magnificent sway.