I think the origin of the phrase is from the conception of Leo Blair. Cherie told the world that it was unplanned - the Blairs were on their annual Prime Ministerial visit to the Queen at Balmoral, and since they knew from previous visits that their luggage would be unpacked by the Queen's footmen and were embarrassed at them seeing her IUD, and they thought she was into her menopause, they did not take one. And the result was Leo.
And the result of the TMI was presumably serious psychological problems for Leo - imagine knowing, and knowing that the whole world knows, that you are the result of an accident because your mum was too embarrassed to take a contraceptive to the Queen's.