Convert String with Dot or Comma as decimal separator to number in JavaScript

Question

An input element contains numbers a where comma or dot is used as decimal separator and space may be used to group thousands like this:

'1,2'
'110 000,23'
'100 1.23'

How would one convert them to a float number in the browser using JavaScript?

jQuery and jQuery UI are used. Number(string) returns NaN and parseFloat() stops on first space or comma.