"We are not actually the lawyers for the men who are detained in Belmarsh prison. But under English law, it is possible to make a submission to the law lords, asking if you can present evidence on behalf of the men, because you think that the case is of great national importance. Law lords agreed that we did have a case to make," Hugill said.
Hugill explains that his organization is not the only one that has started this challenge.
"There are several parties. There are two different lawyers acting for the detainees. There is ourselves, making the general point, and also Amnesty International are making representations, as well. So there, in fact, are four of us bringing the case," Hugill said.
The hearing took place in a committee room at the House of Lords, the British Parliament's upper chamber. It lasted four days and was formally completed today.
The challengers argue "it is unacceptable in a democracy committed to the principles of equality and antidiscrimination to single out foreign nationals," when the same measures do not apply to the country's own citizens.
The government -- represented by its top lawyer, Attorney General Lord Goldsmith -- presented a different view. Goldsmith argued that an "unprecedented form of terrorism" demands a robust response from the government to what he called this "new and intense threat to the nation."
Hugill finds this argument unacceptable. "I don't have any sympathy with that argument at all. That is the argument that nondemocratic states always make. They always say, 'You have to trust us. We know better than you.' The reason that democratic societies have juries, have court systems, is precisely to stop that happening," Hugill said.
Some experts say part of the government's problem may be a lack of strong evidence, or that such evidence is too sensitive.
Paul Wilkinson is the chairman of the Centre for the Study of Terrorism and Political Violence at the University of St. Andrews in Scotland.
"It is quite clear that there is a considerable amount of intelligence that has been gathered about these individuals. But intelligence doesn't necessarily translate into evidence that would stand up in a court of law," Wilkinson said.
Magnus Ranstorp, director of the Centre for the Study of Terrorism and Political Violence, says it is a delicate balance act for the British government -- maintaining respect for human rights while also doing everything to protect the safety of its citizens.
"The judicial process is a very lengthy one, and perhaps some would argue that it needs to be speeded up. Maintaining security, following intelligence leads coming from not only Europe but also worldwide -- the British have a responsibility to do that, and to prosecute. But you have to balance the security and civil liberties," Ranstorp said.
Ranstorp notes that the government has indeed indicated that some of the evidence against the nine suspects cannot be presented in an open court.
Hugill, however, is confident any problems concerning the sensitivity of evidence can easily be overcome.
"If there is information which is so sensitive that the government feels that it cannot present it in an open court, we would have no objection to the case being held in camera [in a judge's private chambers], so that would be a ban on media coverage of that sensitive information. We would not object to that at all," Hugill said.
Hugill points out that members of juries are bound by law not to reveal sensitive information to the public.
A ruling by the high court judges is not expected for at least a month.