The three men deny any criminal conduct. They have also insisted that, if there is a case against them, it should be tried in England because that is where, at least in part, the alleged offences occurred.
Enron, a high-flying US energy trading firm, collapsed in 2001 under billions of dollars of debt, in what was at the time the biggest corporate bankruptcy in US history.
Former Enron executives Kenneth Lay, 64, and Jeffrey Skilling, 52, have been convicted of setting up an elaborate scheme to deceive investors over Enron’s crumbling finances. They are due to be sentenced in October.
Dominic Grieve, legal affairs critic for the main opposition Conservative party, said he was concerned about "the sweeping use of extradition powers" to dispatch to the United States suspects in white collar crime cases "which appear, on the face of it, to have little to do with the US".
"In the case of the NatWest Three, the alleged victim is a British bank and no criminal proceedings have been brought against the defendants in this country. This must give rise to considerable disquiet."