Let us begin with brake release. First off, a skidding tyre has less authority to affect direction. If skidding from the start, the left bogie is having less effect on direction than the right. That means the a/c will tend right, and may explain the Captain's initial left ruddering. (with four healthy engines))
Concorde engines didn't all spool up at the same speed (3 + 1 iirc) so this was normal.