The issue isn't The Wealthy having all the money. The issue is technology that will actively remove jobs. It doesn't matter if minimum wage is 90 pounds an hour if you don't have a job. An automated train isn't The Wealthy stealing money. It is a conductor out of work because their job could be handled by a raspberry pi.
Basic Income is a theoretical concept (been implemented in small, borderline meaningless, experiments) to combat that. Everyone gets a bare minimum "salary" regardless of if they work. That covers cost of living (how much more varies). Then, those with jobs have the potential to earn a lot more (incentive to work) on top of that.
What Thomas Piketty proposes wouldn't address the lack of income to those put out of work by technology but could, possibly, help to pay for solutions that would.