You may have read this complaint in these pages before: British music is badly underperformed — too infrequently programmed. This is true in the orchestral realm, the chamber-music realm, the song realm, etc. (And that includes the operatic.) If there is one man to remedy it, it is Sir Colin Davis, the octogenarian conductor who led the New York Philharmonic on Saturday night.

At the beginning of the 2005–06 season, he brought the London Symphony Orchestra to Avery Fisher Hall, for three concerts. The music included Vaughan Williams’s Symphony No. 6 — and that performance was well-nigh definitive. In this same hall on Saturday night, Sir Colin led the New Yorkers in another Vaughan Williams symphony: No. 4 (composed in the early 1930s).

This is not the best of the composer’s nine symphonies. (Always nine, huh?) But it is a striking work — and Sir Colin turned on his usual understanding, musicality, and leadership.

In general, this is not a gentle, typically reflective British symphony. No, it is often burly and loud — even rude. Under Sir Colin, the first movement billowed and crashed. The Philharmonic responded well to this frequent guest: grasping his intent, following through. The second movement, which is slowish, featured alluring melodies over a pizzicato pulse. And it closed with some unusually sensuous flute playing.

The third movement is a scherzo, raucous and yawping — here, the Philharmonic was excitingly virtuosic. The brass were sturdy athletes; the woodwinds surefooted dancers. Sir Colin egged everyone on. As for the last movement, which has a “fugue epilogue,” as Vaughan Williams calls it — actually, he uses the Italian: “epilogo fugato” — it can get messy and cacophonous. But, under Sir Colin, it was clear and orderly — while still having its visceral thrill.

The symphony composed the second half of the program. The first was all-Beethoven, starting with the “Leonore” Overture No. 2. This is one of the overtures that Beethoven wrote for his opera “Fidelio,” which was long aborning. Incidentally, one of the best-conducted recordings of this opera is Sir Colin’s — on RCA Victor. His “Leonore” Overture No. 2 on Saturday night was peculiar — but effective. The first section was slow, stretched out to the max. But it was also well calculated. It was filled with Beethoven’s drama, and some of that drama lay in Sir Colin’s gigantic rests. The transition to the faster section was terribly exciting.

Throughout the overture, the Philharmonic committed many more stumbles than strictly necessary. But tidiness was not the point of this particular account. And the overture was followed by a piano concerto — No. 4 in G major, Op. 58. The soloist was Richard Goode, a pianist who is particularly well suited to this work: The concerto is smooth and lyrical, and so is Mr. Goode. In fact, I have referred to him as “Mr. Smooth” — he has zero pianistic rough edges.

And, indeed, he did much beautiful and apposite playing. But he was not at his best in the first movement. Some of his passagework was rushed and sloppy. Sitting so close to the keyboard, Mr. Goode appeared constricted, without enough room. And he was often too retiring. In honor of “Gypsy,” now playing on Broadway, I thought of the famous line, “Sing out, Louise!”

Also, something strange happened at the end of the first movement: Mr. Goode held Beethoven’s chords, pedaling through them, not releasing them. This struck me as both gimmicky and unmusical.

But Mr. Goode has a fine musical mind, as we heard in the first-movement cadenza — and as we heard in the entire second movement. Beethoven’s heartbreaking little drama had its true effect. And Mr. Goode sculpted the last phrase beautifully: So many pianists botch it. (For example, the closing E does not get under the F sharp.)

And the final movement, that delightful rondo? It was not real clean — strange, from Mr. Goode — but it had plenty of character. And the pianist released Beethoven’s final chords.

By the way, Mr. Goode seems to be growing his hair — a pure white — to Franz Liszt level. Very pianistic. And, of course, Colin Davis owns a mass of pure-white hair. The sight of it on a podium is one of the most reassuring things in music. Let’s enjoy it while we can.