The Daily Mail's Jan Moir said the Stones had somehow beaten the aging process: "You might imagine that they had been worn down by life, by wives, by arthritis, by scandals old and new, by drugs, but no - they seemed indestructible." She said their swampy, gritty sound remains unique after half a century.
Daily Telegraph reviewer Neil McCormick said the band exceeded all expectations. He described the weaving of the guitarists, mixed with Jagger's blues harmonica, as a wonder.
"When looking for the secret of the Stones, it is perhaps that they actually listen to each other while they play, and almost lose themselves in it, while their brilliant frontman keeps it all together," he wrote.
Ebullient fans agreed with this assessment, as did the Guardian newspaper, which gave the performance four out of five stars.
Jagger, in skin-tight black pants, a sparkly tie, and a matching checked jacket and hat, took time out from singing to thank the crowd for its loyalty.
"It's amazing that we're still doing this, and it's amazing that you're still buying our records and coming to our shows," he said. "Thank you, thank you, thank you."
Lead guitarist Keith Richards, whose survival has surprised many who thought he would succumb to drugs and drink, was blunter: "We made it," he said. "I'm happy to see you. I'm happy to see anybody."
But the band's fiery music was no joke, fueled by strong guest appearances by Taylor; Mary J. Blige, who shook the house in a duet with Jagger on "Gimme Shelter"; and Jeff Beck.
The 50th-anniversary show, which will be followed by one more in London, then three U.S. shows (Brooklyn, N.Y., and Newark, N.J.), lacked some of the band's customary bravado - the "world's greatest rock-and-roll band" intro was shelved - and there were some rare nostalgic touches.
The concert began with some early Stones' numbers rarely heard in concert, including the band's cover of the Lennon-McCartney rocker "I Wanna Be Your Man" and a cover of "It's All Over Now," written by Bobby Womack and Shirley Womack.
Jagger seemed more mellow than usual. He said 2012 had been a terrific year for Britain and that the Stones nearly missed the boat, playing no role in the celebration of the Queen's Diamond Jubilee, the London Olympics, or the new James Bond film.
"We just got in under the wire," he said. "We feel pretty good."