Lawyers for three people who have campaigned for the right to die are taking their case to the UK's highest court this week, arguing that medical staff should be allowed to assist those physically unable to end their own lives.

Nine supreme court justices are considering claims that there should no longer be an effective ban on the severely incapacitated from seeking a "dignified and humane" death.

The cases have been brought by Jane Nicklinson, whose husband, Tony, died in August 2012 after losing a high court battle, and Paul Lamb, 58, who has spent the past 23 years immobile apart from his right hand following a road accident.

A third claimant, known to the court only as "Martin", who is 49, is challenging the policy of the director of public prosecution (DPP) that only close friends and family can take individuals to a suicide clinic abroad.

The large number of judges on the supreme court bench indicates the legal significance of the hearing. It is due to last four days; judgment is expected to be reserved until the new year.

Nicklinson and Lamb are appealing against a ruling by the court of appeal earlier this year that a blanket ban on assisted suicide or euthanasia is a "proportionate interference" with their rights under article 8 of the European convention on human rights, which guarantees respect for private and family life. The appeal court said it was for parliament, not the courts, to change the law.

Paul Bowen QC, for Nicklinson and Lamb, told the supreme court on Monday that the present situation had "extraordinary and cruel consequences" for some disabled people whose family and friends were unable or unwilling to help.

It meant, Bowen explained, that they could not end their "unbearable suffering" with dignity. The only option was a "less dignified" death which might put others at risk of prosecution.

The supreme court is being asked to decide whether a prohibition on assisted suicide, set out in the 1961 Suicide Act, is compatible with article 8.

Nicklinson and Lamb maintain that the law should include a "defence of necessity" where doctors should be allowed to assist suicide when people have a "voluntary, clear, settled and informed" wish to end their life but cannot do so without medical assistance.

Bowen said he was not asking the court to change the law, merely to declare that the act was incompatible with the European convention on human rights. Such a ruling would then require parliament to legislate on the issue.

Present legal restrictions fall disproportionately on "a small group of disabled people" resulting in discrimination against them, Bowen added. "The current regime is less safe than in other countries where the practice is permitted … No doctor will provide assistance when they face the prospect of prosecution."

Health workers fear even discussing the issue with patients and the only medical assessment of a patient's ability to make a reasoned decision is after death in the context of a criminal investigation, Bowen explained.

Before the hearing on Monday, Nicklinson, 58, of Melksham, Wiltshire, said she and fellow campaigners had done all they could. "I'm pleased to see that nine judges are sitting. They clearly mean business. I'm hopeful. I'm confident we have done everything we can. We feel very strongly … Something needs to be done."

Lamb, who used to be a builder and lives in Bramley, near Leeds, said: "A change in the law would mean more to me than a million dollars. A change in the law would be a massive step in the right direction. You would not do this with pets. Pets have got the law in their favour."

The supreme court justices are considering a counter-appeal by the new DPP, Alison Saunders, against the appeal court's decision that the prosecution guidelines should be reviewed and clarified in relation to the claim brought by "Martin".

At the time, the then DPP, Keir Starmer QC, said he believed it would be sensible "to have the benefit of the views of the supreme court before any amendments are made to the DPP's guidelines in this important and sensitive area of the law".

The British Humanist Association (BHA), which has intervened in earlier hearings and supports Nicklinson and Lamb's claims, believes there is public support for a change in the law on assisted dying.

It pointed to a YouGov poll last year that found that 81% of UK adults backed the idea that mentally competent individuals with incurable or terminal diseases who wished to end their lives should be able to receive medical assistance without those assisting them facing prosecution.

Pavan Dhaliwal, of BHA, said: "This legal case is necessary to establish that being able to die, with dignity, in a manner of our choosing, should be understood to be a fundamental human right.

"We hope that the supreme court judges will listen to the large majority in this country which supports a change in the law on assisted dying, and rule in favour of the right to a doctor-assisted death for the permanently incapacitated and incurably suffering."

The case continues.