More than 200,000 people have signed our online petition, which triggered an emotional Westminster Hall discussion that lasted for almost three hours yesterday.
There was standing room only as MPs packed the room and 34 were called on to speak, with the majority expressing support for assisted dying.
Dame Esther, 83, who watched from home due to her stage four lung cancer, was deeply moved by several of them sharing personal experiences that influenced their views.
However, the Childline founder expressed disappointment that others who opposed assisted dying appeared "implacable" and unwilling to consider evidence from countries that successfully introduced it.
Dame Esther urged supporters to keep fighting, saying: "I want to thank those wonderful 200,000 signatories who enabled this important debate to happen but we need them now more than ever.
"When and if a parliamentary debate is scheduled, with a free vote which could bring about this crucial change in the law, we need their help.
"We need them to write to their MPs with their stories. Describe their experience. Those are the most powerful and most persuasive arguments."
Her daughter Rebecca Wilcox added: "Whilst it was somewhat frustrating listening to a few MPs spouting opinion over fact there were speakers who brought us hope. And it truly feels like compassionate common sense could prevail and a change in the law might come about thanks to you."
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