Although it was perhaps 15 minutes too long, the last date on a brief world tour by these master songsmiths was a dream ticket, in which the two men performed songs from their recent album, Painted From Memory, and plundered two of popular music's finest back catalogues.
When it came to the vintage material, it was the old devil who had the best tunes ("Alfie," "Do You Know the Way to San Jose," "Anyone Who Had a Heart"), but Costello wasn't far behind.
As it first emerged that Costello and Bacharach were working together, attention was focused on the alleged unlikeliness of the partnership: the punkish Costello and the shy, elegant, classically trained 70-year-old would surely never find a meeting point. To me, however, it seems perfectly natural that they should collaborate.
The son of a big-band leader, Costello (who was never really part of the punk thing - he just had narrow trousers and a sneer) has always been a fan and was covering Bacharach and Hal David's "I Just Don't Know What to Do with Myself" 20 years ago, while both men have a highly developed gift, or in Bacharach's case a genius, for writing memorable pop tunes. Bacharach showed when he was last in London that he is hardly stuck in the past, when he teamed up with Noel Gallagher.
The album that resulted from Burt and Elvis's collaboration is something of a gem: a rich, brooding, structurally complex but (crucially) hummable collection of songs, with stirring choruses and rather dark lyrics (from, of course, old misery guts Costello). Here Costello sang the songs beautifully, accompanied by band and string section, with Bacharach on piano and conducting.
"This House Is Empty Now" was bleak but touching; on "I Still Have That Other Girl" his voice crackled with emotion; "Toledo" illustrated the pair's knack for writing numbers that sound as though they've been around for ever.
But it was the old songs that really did the business, as each man had his own solo spot. Bacharach, mercifully, didn't do much singing during his (he hasn't got much of a voice, and he also seems to suffer from a nervous dry throat), but left it to the backing vocalists. They took it in turns to sing some of the finest tunes ever written: "I Say a Little Prayer," "Twenty-four Hours from Tulsa," "Trains and Boats and Planes" (classic Bacharach, with its simple tune and complex tango rhythm).
Costello's highlights, meanwhile, were "Accidents Will Happen" and "Alison," both performed with new string arrangements. The only misjudgment was that he should have ditched his guitar on "Almost Blue" — with Steve Nieve on piano, there was no need for extra embellishment.
Costello also sang what was probably the finest rendition I have ever heard of "I Just Don't Know What to Do with Myself." Dressed in a tuxedo and bow tie, cradling the microphone stand, he seemed completely in his element as he swooned, crooned and simpered his way through an extraordinarily delicate and subtle reading of the song made famous by Dusty Springfield in 1964.
This was popular music at its finest: neither young nor old, but ageless, and timeless.