The blind peer recounted how he went awry during his induction as a member of the Privy Council, which advises the monarch, and how she had helped “shift me round”.
He revealed the anecdote as peers paid their respects at Westminster to the late Queen, following her death aged 96.
Lord Blunkett, who uses a guide dog, spoke about how he had been “quite nervous” ahead of the ceremony to become a Privy Counsellor 25 years ago.
Her Majesty in a gracious and careful and never patronising way managed to gently - by touching my arm - shift me round
He said: “I knew I couldn’t actually drag the dog across the floor because dogs aren’t very good at showing you where to kneel on cushions. They are brilliant at all kinds of other things but that isn’t one of them.
“So I left the dog with Jack Straw and I moved across the room and I did manage to hit the cushion, but facing the wrong way.
“Her Majesty in a gracious and careful and never patronising way managed to gently – by touching my arm – shift me round so that I could just brush her hand.”
On a separate occasion, he recalled the Corgi-loving Queen visiting Sheffield ahead of his retirement as the city’s longest serving MP.
Sitting at lunch with her, Lord Blunkett said: “There was a silence and I thought I would fill it, inappropriately as it turned out, by saying to her ‘Your Majesty, I have been reading in the papers that the breed of Corgi is dying out’.
“There was a tremendous pause and Her Majesty then did what she did so cleverly and so appropriately putting me down.
“‘Mr Blunkett,’ she said ‘Of all people you should know not to believe what you read in the newspapers’.”
Lord Blunkett, who served as education secretary, home secretary and work and pension secretary under former prime minister Tony Blair, was forced to resign from cabinet posts twice after finding himself in the media spotlight.
Paying tribute to the Queen, Lord Blunkett said: “All of us in public life, in one way or another, hope to leave a tiny footprint, some small legacy behind us.
“But Her Majesty strode as a colossus through decades and generations dealing with the most incredible personal and public events and taking on those challenges with fortitude.”
“Our Queen will be deeply missed but her guidance and example will carry I am absolutely sure into the life and work of His Majesty King Charles III, through turbulent and sometimes difficult times, displaying his great strength and compassion which I have experienced and of course understanding that duty to us as a nation.”
He added: “Of course, our respect requires our mourning but in my view we need to celebrate and rejoice in the life of Elizabeth II. We need to lift people as well as mourn.”