Asked at a conference fringe meeting if she pinched herself about her rapid progress up the political ladder she replied: "I do."
She said: "I wake up in the morning and think my God I'm in the Cabinet! Blimey!"
The question of whether she would lead the Labour party prompted a torrent of loud nervous laughter and a modest: "I just don't think it is possible whatsoever, I have got a huge job on my hands at the moment. Even thinking about that is impossible."
Ms Kelly revealed the influence of her early upbringing as a Catholic in Northern Ireland, where families like hers had to try to break into non-traditional professions.
"It has given me an acute sense on what it has been like actually to be the underdog in society," said the Oxford-educated former public school girl.
The Education Secretary admitted earlier this month that she was having discussions about progressive taxation at the age of six.