"I opened the door to Prescott and showed him in. It was the first time I'd met him.
"As he came through the door, he pushed me quite forcefully against the wall and put his hand up my skirt. Things were different in those days.
"It was not uncommon for men to take their chances. He was just trying it on. There was no big fuss.
"I just rebuffed him politely. He shrugged and winked and we all carried on. But from that day I knew what sort of man he was."
Lord Prescott's emphatic denial was made when discussing an invitation from Mr Mitchell for he and his wife to come to a dinner to mark his retirement as an MP and can be revealed for the first time.
The peer said: "This is the man whose wife accused me of putting my hand up her skirt bloody thirty years ago.
"She decides, with all this thing about sex coming out, to say that I came into the house, walked in through the door, shoved her against the wall and put my hand up her skirt."
At the time Lord Prescott said he told Mr Mitchell: "This is just not true." Mr Mitchell replied: "She says it."
Lord Prescott added: "I had to say, 'do you believe it Austin?' Have you seen his wife? Built like a bloody barn door, if I threw her against the wall, the fxxking house would fall down."
Last night the peer strongly denied ever sexually assaulting Miss McDougall. He said: "She never said anything [in 1978] because I never did anything. How is it that she waited 30 years to make a story?"
In response to Lord Prescott's comments, Mr Mitchell told The Daily Telegraph: "I have always considered John Prescott a friend, but his reaction to my invitation to come to my farewell dinner was churlish in the extreme.
"So I am assuming he is a wounded man at the moment and therefore best left alone."
The peer has previously said his former mistress Miss Temple's recollections about their affair in a Sunday paper were "simply untrue" and "motivated by a desire to maximise financial gain".
When their relationship was revealed in 2006, Lord Prescott said: ''I did have a relationship with [Miss Temple] which I regret.
"It ended some time ago. I have discussed this fully with my wife Pauline who is devastated by the news."
Mr Miliband had brought the veteran Labour peer in as an adviser on climate change, to help him negotiate the UN climate change summit in Paris.