Mencap president Lord Rix urged the speaker of the House of Lords to push through legislation allowing those in his situation to be assisted to die.
He had previously opposed an assisted dying law, but said his illness has left him "like a beached whale" and in constant discomfort.
"My position has changed," he wrote to Baroness D'Souza.
Stage and TV actor Lord Rix, who specialised in post-war "Whitehall farce" comedies, is receiving 24-hour care in a retirement home.
"My position has changed. As a dying man, who has been dying now for several weeks, I am only too conscious that the laws of this country make it impossible for people like me to be helped on their way, even though the family is supportive of this position and everything that needs to be done has been dealt with.
"Unhappily, my body seems to be constructed in such a way that it keeps me alive in great discomfort when all I want is to be allowed to slip into a sleep, peacefully, legally and without any threat to the medical or nursing profession.
"I am sure there are many others like me who having finished with life wish their life to finish.
"Only with a legal euthanasia Bill on the statute books will the many people who find themselves in the same situation as me be able to slip away peacefully in their sleep instead of dreading the night."
The crossbench peer voted against an Assisted Dying Bill in 2006 because of concerns that people with learning disabilities might become the unwilling victims of euthanasia.  He has been a prominent campaigner for people with learning disabilities after his daughter was born with Down's syndrome.
He said his children were "absolutely supportive" of his decision and that he has "wrapped up" his affairs and was "ready to go" to "put an end to this misery, pain and discomfort".
"I can't do anything but lie here thinking 'Oh Christ, why am I still here?' They won't let me die and that's all I want to do," he said.
He added the doctors and nurses "do their best for me" but that it was "not good enough because what I want is to die, and the law stops them from helping me with that".
He had discussed with his children the possibility of travelling to the Dignitas clinic in Switzerland, but felt it would be "unfair to them to push them into a situation where they are helping me to die".
Lord Rix said he had not been given an estimate from doctors as to how long he will live, adding: "I think it's wrong that people like me are stranded like this.
"I'm not looking for something that helps me only, I'm thinking of all the other people who must be in the same dreadful position."
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Terminally ill actor and disability campaigner Brian Rix, 92, has said the law on assisted dying needs changing.