Answer: The Beatles were officially formed in Liverpool in 1960, whilst The Rolling Stones were formed in London in 1962.
As for Carnaby connections, there have been many over the years, including Paul McCartney meeting his future wife Linda Eastman in The Bag O Nails, and more recently, the 2012 Christmas installations celebrating the Rolling Stones 50th Anniversary (the band have been frequent visitors to shops in Carnaby Street over the years, and have rehearsed for live shows just round the corner in Broadwick Street).
Thanks again to Wikipedia.