If a person is either sectioned or mentally unstable are they liable to face prosecution for an offence?

Thats a real can of worms....Yes and no.

Essentially if a person is considered to enjoy been mentally competent at the time of the offence and understood what they be doing they are considered responsible. If they are mentally incapable of understanding the implications of their actions consequently they are considered to not be legally responsible. There is a huge grey area here tho, and really its upto the experts who perform the diagnosis and the intercede to decide mental capacity.
Okay, we enjoy "legally insane", "Mentally unfit", and "mentally/emotionally unstable". They are not the same thing.
If you are deem mentally unsound by mental health workers, it simply means that you are emotionally disturbed. This alone does not exempt you from criminal liability. You can be an absolute raving lunatic, but still be reasonably culpable for your crimes.
"Mentally Unfit" is a legal term referring to a person who is not fit to stand trial. It requires that the personality be unable to understand the charges against them and be unable to assist within their own defense. This will NOT dismiss your criminal charges. It will simply get you institutionalized until such time as you are fit to stand trial. If you recover, you go to court. If you don't you spend the rest of your life span making pretty pictures with your own feces on the walls of your padded cell.
"Legally Insane", or more accurately, a finding of "Not Guilty by Reason of Insanity" requires that you be unable to determine right from wrong AND be unqualified to control your actions. If you can do one of those things, you're still guilty. Otherwise, you go to a mental institution until it is determined that you are no longer a danger to yourself or others.
Many, abundant people who are schizophrenic or have other serious emotional disorders stand trial and are found guilty because their mental disease did not preclude them from being able to control their actions nor did it preclude them from individual able to determine right from wrong.
They can plead noncompismentis to not receive jailtime I agree with misskitt!!
(UK) If their psychologist give evidence that they be sectionable at the time the offence was committed then they are not liable for any misdemeanour committed during the time the balance of their mental health was artificial. The lack the necessary mens rea to commit a crime.

(USA) Christ knows. The States ruled that Charlie Manson be too crazy to defend himself but not crazy enough to evade prosectution. Certainly in the seventies some states would rule "not guilty by cause of insanity" and some would rule "guilty but insane". The US has never been very dutiful with loonies, I'm afraid.
no they was not in control when they broke the law, but depending on what they are resembling or done they can be sectioned under the mental health accomplishment and be kept longer then they would if they went to prison.

regards x kitti x
Most unlikely if already sectioned. It may head to sectioning in the other case, fairly than a conviction. People under Section or Mental Health Act, cannot face trial for criminal offences, because they are deem to be mentally infirm.
i think it depends on the offence and if the party is a danger. for instance, peter sutcliff was deemed mentally unstable but he be clearly a danger so the put him in a secure hospital a bit than a jail. If they are sectioned then they will be held surrounded by secure accommodation and could not face trial. If they are mentally unstable next I believe they could face prosecution but much would depend upon how the courts react to their perceived mental instability.