Record numbers of Britons who are suffering from terminal illnesses are queueing up for assisted suicide at the controversial Swiss clinic Dignitas, the Observer can reveal.

Almost 800 have taken the first step to taking their lives by becoming members of Dignitas, and 34 men and women, who feel their suffering has become unbearable, are ready to travel to Zurich and take a lethal drug overdose.

The tenfold increase in the number of Britons who have joined Dignitas since 2002 will raise questions about the law that bans assisted suicide in Britain.

On Tuesday, 46-year-old Debbie Purdy, who suffers from progressive multiple sclerosis, will go to the House of Lords, the UK's highest court, asking it to determine whether her husband Omar Puente will be prosecuted if he helps her to travel abroad to die.

The 34 Britons given what Dignitas calls a "provisional green light" to die have provided documentary evidence of their condition and been interviewed by both a doctor and Ludwig Minelli, the founder of Dignitas, and satisfied them that they are mentally fit to make such a decision.

One of the 34 is due to undertake an accompanied suicide very soon. Four have already secured fixed dates for their deaths, but adjourned them. The remaining 29 have not yet arranged a specific date.

A further four British people failed to get Dignitas's permission after the Swiss doctor who examines all applicants said they should not be helped, either because they did not have an incurable illness or were judged not of sound enough mind to reach such a decision.

Dignitas figures also show that 15 Britons took their lives there in 2003, 26 in 2006, eight in the first five months of 2008 and 23 in the past 12 months.

The disclosures will reopen the highly charged debate about euthanasia. This week, an influential group of peers, led by two former ministers in Tony Blair's cabinet, will seek to end what they see as the outdated and inhumane situation in which relatives or friends risk up to 14 years in prison if they travel with a loved one undertaking assisted dying overseas.

The peers - led by Lord Falconer, a former lord chancellor, and Baroness Jay, a former leader of the House of Lords - will table an amendment to the Coroners and Justice Bill in an attempt to lift the threat of prosecution from people in England and Wales who want to support someone in their final moments.

The 1961 Suicide Act criminalises anyone who aids, abets, counsels or procures someone else's suicide, and some relatives who have travelled have been questioned by police on their return. However, government law officers have already admitted that no one who goes abroad for that purpose is likely to face prosecution.

"It's a tragic anomaly that people who are giving a last loving assistance to a loved one find themselves under threat of 14 years' imprisonment if they do," Jay said last night. "Having made the very difficult decision to travel abroad to somewhere like Switzerland, where assisted dying is legal, someone would want the sort of support they would expect here from a husband, wife or loved one. The law in this area is a fudge and parliamentarians are lagging behind public opinion on this."

Prominent peers with legal or medical backgrounds are backing the move, including Lib Dem barrister Lord Lester, Baroness Greengross, the former head of Age Concern England, and Lord (Naren) Patel, chairman of the National Patient Safety Agency.

If they win - and they are increasingly confident - it would force the government to take a view. It used parliamentary procedure to prevent voting in March on an identical amendment in the Commons, which had been proposed by Patricia Hewitt, the health secretary until 2007.

Lesley Close, who travelled to Dignitas with her brother, John, in 2003 when he ended a life overshadowed by motor neurone disease, said: "More and more British people will be joining Dignitas and travelling to Switzerland to die because more people are aware of the compassionate and peaceful death you can achieve there.

"The interest in Dignitas among Britons underlines the case for reform of the law here. We need the same facility here [as Dignitas]. It's a perfectly rational and humane decision to end your life if you are suffering intolerably at the end of a terminal illness."

Sarah Wootton, chief executive of Dignity in Dying, which campaigns for a new right to assisted dying, said: "These figures show that the situation in this country is forcing people into difficult and dangerous decisions - to go abroad for an assisted death, or ask their doctor or a relative to help them die, or to attempt suicide themselves, some of which end up being botched.

"There is clearly a growing demand in this country for a well regulated, legal right for people with terminal illness, who are mentally competent, to end their life if they choose to."