Natalie Cole with the BBC Big Band, Langham Hilton, London

The King is dead, long live Natalie

The late Nat "King" Cole's younger brother Freddy once had a hit with a tune called "I'm not my brother, I'm me". Natalie Cole could be forgiven for voicing similar sentiments, for the jazz world seems to be reluctant to accord her a place in her own right. The triple-volume New Grove Dictionary of Jazz grants her no entry, nor do the collected works of that doyen of critics, Whitney Balliett, make reference to her.

Is it because she doesn't play as well as sing, or because she recorded an album of posthumous duets with her father? Whatever the answer, it's a curious situation, since Natalie Cole has tremendous chops. Her style, a little on the showy side, may lead some to class her among the "singer" rather than the "jazz singer" category. But, as her considerable scatting abilities demonstrate, that is surely a mistake.

This invitation-only event in the ballroom of the Langham Hilton was a sumptuous affair, her own backing quartet and the BBC Big Band being augmented by a string section, French horns, vibes and even a harp. The luxury of witnessing so lavish an orchestra in such an intimate setting may have been too much for the palates of those with more ascetic tastes. But I'd say that anyone of that opinion should wise up and learn to love their pudding.

After the first four numbers, during which the balance wasn't quite right and the band almost drowned her out, Cole settled into a quieter set. "Route 66", in which she was backed just by her quartet, provided the perfect opportunity to hear the full glory of her voice. Like molasses dripping from a spoon, it ebbed and flowed, different shades reflecting and sparkling off as if caught in the sun.

On "What a Difference a Day Makes", she began accompanied only by the double bass. The rhythm section came in on the next eight, and then the horns joined in slowly, almost behind the beat, locking together with all the inexorable momentum of an ocean liner. The BBC Big Band would have earned a tip of Count Basie's hat, so hard and low did they swing.

Most of the material was pretty much what you'd expect – standards, a duet with her father on "Unforgettable" that could have been schmaltzy but was actually extremely moving – with one or two surprises: a Michael Franks number, "Tell Me All About It" (do we detect the influence of their mutual producer, Tommy LiPuma?), and the underperformed ballad "I'm Glad There Is You".

OK, Natalie Cole is hardly cutting edge. But to hear her fabulous voice backed by the kind of production values taken for granted in the United States is a treat. I'd advise you to go back for seconds.

This concert will be broadcast in two parts, on 11 and 18 November, at 10pm on BBC Radio 2