No. 101 on the left and 100 on the right are discreetly occupied by high-profile financial organisations.
The square is named after Sir John Barbirolli, ex-conductor of the Hallé orchestra. Their current home, the Bridgewater Hall, is out of view to the right, and in the next image.
The polished white marble 'pebble' is 'Ishinki-Touchstone'.