My understanding is that BA still own it.
It is mainly the dear paperwork that keeps Concorde from flying. If one only considers the TU-144 that sat in storage for who knows how many years before the Russians got it flying again.
Have to disagree there.
It is money (lots of it) that is keeping it firmly grounded. Huge quantities would be required to a, get it airworthy and b, keep it that way.
The TU-144 had government (and NASA) backing, Not something that is likely to happen soon over here.