Can you have my body? What about my mind?

I'm currently working with two people who want to take out writs of habeas corpus (literally, 'you may have the body'). This is the right people have to ask the Court to test whether they are lawfully imprisoned. There is quite a nice historical article in the BBC News Magazine from a year ago: A brief history of habeas corpus.

In both cases the solicitors involved don't seem to be taking these requests seriously. According to a quick internet search the law of habeas corpus is rarely used in the UK today, partly because it is being superceded (or perhaps obscured?) by other legislation (e.g. the Police and Criminal Evidence Act 1984 which sets out the law for police custody, and the Anti-terrorism, Crime and Security Act 2001 which prevents suspected terrorists from using the law, as per above article).

Several solicitors firms do mention habeas corpus work on their websites, but I wonder if the approach is gradually falling from people's minds. This is not helped by comments like this from Lord Bingham in 1999 when he was Lord Chief Justice:

"The concurrent application for habeas corpus was wholly unnecessary and served only to increase costs unnecessarily. It should not have been made."

In the same year Lord Justice Brown, in the Annual Lecture of the Administrative Law Bar Association said:

"I have come to regard habeas corpus in its present form as a defective process, unnecessarily and unsuccessfully competing with judicial review. No one, I think, would defend the law of habeas corpus as it operates today." Link

What interests me in these cases is the desparation of the people involved, and their certainty that the system has detained them unjustly but will never let them go. Both say with some persuasiveness that they should not be detained in hospital, that they are not receiving treatment (or it's not working). The hospital may have their bodies, and there may be nothing much that can be done - but they certainly don't have their minds...

So despite this bit of knowledge that I've gained today, should I support their applications for habeas corpus as an independent advocate, as this is what they want to do?