Paul Lamb, a paralysed former builder and Jane Nicklinson, the widow of a man who had 'locked-in' syndrome brought the case.
They claimed stopping doctors from helping people who wanted to die breached their human rights - but a group of judges disagreed.
On the News Hour Dr Andrew Ferguson from the group Care Not Killing told Premier's Antony Bushfield he was pleased with the outcome.
The Church of England has also responded to the outcome.Revd Dr Brendan McCarthy, National Adviser on medical ethics and health and social care policy for the Archbishops' Council, said: "We welcome the judgment of the Supreme Court and the emphasis it has placed on the need for the law to protect vulnerable individuals.
"We recognise the distress that this judgment will cause some individuals but we believe that any other judgment would have resulted in even greater distress for even greater numbers of people.
"But some are vowing to continue their campaign to have assisted suicide legalised."
Andrew Copson, Chief Executive of the British Humanist Association, said: "So long as there are strict safeguards, it is our moral duty as a society to give assistance to mentally competent adults who are suffering incurably, permanently incapacitated, and have made a clear and informed decision to end their life but are unable to do so independently.
"We will continue our work to see this happen at last, and are proud to support the brave individuals who continue to bring these cases, overcoming great personal tragedies in order to advance justice and bring about a more humane society."