The terminally ill TV campaigner warned him: "For me, and others like me, it has to happen soon."
The PM had told cancer-stricken Dame Esther, 84, this year that he was in favour of changing the law and would guarantee Parliamentary time to debate the issue.
But he has so far failed to honour that pledge and time is running out. The Childline founder added: "He did say to me rather sweetly - I had a phone call conversation with him that he hoped I would be alive to see the debate.
"I just want to remind him gently, nothing bossy, just quietly, 'Dear Sir Keir, whom I have met and worked with, could you possibly recall your kind words to me and make it come true?""
Last December Dame Esther joined increasing demands for reforms to allow assisted dying, after revealing she had been diagnosed with stage four lung cancer.
The former That's Life! presenter says that "miracle drugs" have extended her time, but she fears her family will be forced to watch her suffer or stay behind in the UK while she travels to the Swiss suicide clinic Dignitas.
Daily Express crusade Give Us Our Last Rights wants terminally ill people in their last six months to be allowed to request medical help to die with dignity. A huge petition was sent to No 10.
A Private Members' Bill on assisted dying is set to be introduced in the Commons after supporter Jake Richards won a place last week in the MPs' lottery to propose new laws.
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