Eight hundred British people are registered with Dignitas, the Swiss clinic that helps the terminally ill end their lives - up 100 since January.
Assisted suicide is illegal in many countries
And in the past six weeks, four Britons have carried out assisted suicides at its Zurich clinic, the voluntary euthanasia group Dignity in Dying said.
The charity wants the law changed to make assisted suicide legal in the UK.
But biomedical ethicist Dr Rob George said it would be preferable to provide better care for the terminally ill.
"By killing a patient you don't kill the problem. This is an issue of care and this is an issue of providing appropriate support," he told BBC News.
"It costs £5 to kill somebody. It costs £500 pounds a week to look after them... We need to be pressuring for decent care in this country. That's the bottom line."
Dignity in Dying's chief executive, Deborah Annetts, predicted that British membership of Dignitas could top 1,000 by the end of the year.
She said she was "shocked and saddened" by the latest deaths but each case demonstrated the need for a change in the law.
"These cases are gathering momentum and a signal is being sent to the British public that if they can afford to go abroad to die, that's no problem. But if you have such help here your relatives could face 14 years or life in prison."
'Dignity in death'
The most recent assisted suicides bring the number of Britons who have travelled to Zurich to end their lives to 54. The first to go public was Reg Crewe in January 2003.
And in January this year, Anne Turner, a retired doctor with a degenerative brain disease, allowed the media to follow her to Zurich where she was helped to die the day before her 67th birthday.
None of the UK cases handled by Dignitas has so far involved any criminal charges, but many have resulted in police investigations.
Discussions on a proposed law change put forward by the former human rights lawyer Joel Joffe in the House of Lords were postponed for six months in June. The medical establishment is against any law change.
Since Dignitas was founded in 1998, it has helped more than 450 people from across Europe to commit suicide. Switzerland's liberal laws on assisted suicide suggest that a person can only be prosecuted if they are acting out of self-interest.