Nigel Kennedy: Proms 2 & 3, Royal Albert Hall, London

Englishness came under close scrutiny in the second Prom of the season: the refulgence of Bax, the mysticism of Finzi, the attitude of Kennedy. Actually, there were two Kennedys at this BBC Concert Orchestra programme under Paul Daniel. The tenor Andrew Kennedy led the BBC Chorus in Gerald Finzi's wonderful setting of Wordsworth's ode, Intimations of Immortality, where past memory and present consciousness meld in music of such rapture that, had the poet been a composer, this is how he would have sounded. Kennedy's rapt tenor attended the words like they were the first and last he would utter.

And then the other Kennedy arrived, punching the air, high-fiving anyone in his path, glad to be among "this great audience" again (well, it had been 21 years). For his second coming in a matter of months, he offered the same "bit of English romantic music". Some bit.

Nobody plays the Elgar Violin Concerto quite like him. This most rhapsodic and improvisational of works demands absolute oneness with its tormented spirit. Nigel Kennedy has grown up with it, he can take it and us to the edge and back. He's so free with it, savouring, caressing, exciting the solo part with an astonishing compendium of rubatos. The spitfire figurations were white hot, moments of reflection brought almost to a pensive standstill.

But nothing was sounded that didn't connect with the feeling behind it. Most extraordinary of all was the accompanied cadenza of the last movement – a backward glance at what has gone before and how it impacts on now. Kennedy played it with a deep sense of unease, but as the final threads were drawn close to silence, there was a profound sense of inner peace. You can't fake that. As for Daniel, he did more than well to survive the white-knuckle ride.

An hour later, Kennedy was back with the five members of his Quintet from Cracow – and the tunes may have been different (his own, actually) but where he took them was hardly light-years away from where he took the Elgar. We sampled the vaguely Celtic – a tribute to Donovan – and the moodily blue; the jazzing was gentle, oddly old-fashioned, with Kennedy like an electrified Grappelli. But it fired up when it got rocky and Kennedy, his electric violin wailing like Jimi Hendrix, invited his guest guitarist Jeff Beck to hit the "Hills of Saturn". Here on Earth, there's only one Kennedy.

BBC Proms continue to 13 September (0845 401 5040)