Ms Short, who was a19-year-old student in Birmingham when they parted, met him only four weeks ago. Toby Graham is now 31, and married with two children,
During an interview with The Independent, she sat with her arm round the handsome man in blue pinstripe. They are obviously besotted with each other, even though they only met a month ago.
"I found out I was pregnant just after my eighteenth birthday. My first thought was my parents - you know I come from a Catholic family. It was different times back then. Everyone was more innocent."
Tony Blair, the Labour leader, who has spoken frequently about the importance of family ties said last night he was thrilled for Ms Short and wished her the best of happiness.
Clare married the child's father and contacted a private adoption agency. "I just thought I would never go back to university, that it would be terrible all round, terrible for the baby, there would be no money, so what I was doing was best for everybody. When they came to take him it was terrible. It's been terrible ever since."
Toby was adopted by John Graham, the director of a public company and his wife, and brought up in comfortably-off conservative family. He went to boarding school, read law at the University of East Anglia and is now a solicitor in the City. He always knew he was adopted and started searching for his natural parents about a year ago. "Officially I've been looking for about a year, but in my mind I always wanted to know and always intended to do this. I suppose what triggered it was when I had a child. I wanted to know what was in the genes."
Clare had registered that she was available if he ever wanted to find her. When she was first contacted, she had registered in another name: "I wanted to protect him from the shock of it being me". She wrote to him, imagining that they would exchange many letters before they finally met.
Toby said: "It was a lovely letter saying that hers was a large and loving family." Clare added: "I tried to fill him in on family history, I said we had lots of teachers, that we were into social reform, a little left. I talked about his father's family and how much I regretted what I had done. Then I explained there was one little problem: 'I've got this slightly high-profile job and we don't want the press crawling around.' He just thought I was being melodramatic."
Ms Short was married for seven years to Toby's father, Andy Moss, who has since remarried and still lives in Birmingham
Toby was desperate to meet up and even though he had heard his mother's voice on her answering machine, he didn't catch her surname or the message saying that she could be contacted at the House of Commons. When they eventually met at her house, he still did not know who she was. "She looked familiar but I said: 'What's this high profile job you've got then?' She said that she was an MP."
Toby's politics have always been Tory. As a student, he even stood as a Tory candidate, but even before he met his mother he was starting to become disillusioned with the Government. Before they met, he described himself to her as a one-nation Tory who was now looking at Blair. Toby may now be more interested in politics, but the priority remains for him to meet his huge family, and for Clare to meet her grandchildren.
Toby says he now "feels much more complete as a person - I know who I am, where I come from, what my roots are". Ms Short holds out his hands. "Look," she beams, "He's definitely got my hands and feels like me inside."
So why has she never talked about it before? "It wasn't a secret. It was a loss and pain in me. I wasn't hiding anything, it was just that this big thing at the centre of my life was painful. Of course, now I feel fabulous - it isn't painful any more. Here he is."
Giving his reaction last night, Mr Blair said: "I am thrilled for Clare that she has met her son and that they have been able to form such a warm relationship ... Clare first told me of this situation some time ago after her son approached her ... I hope the media will be sensitive in their approach to the other people involved."
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