So, Alan Finch was one of the people. He got his case to the Supreme Court in 2009 but I haven't been able to find any records of the hearing.
It is mentioned many times that the Bill was to help transexuals and that gender dysphoria is a medical condition (also how this is such a small number of people).
Official Report of the Grand Committee; 4GC, Lord Filkin:
"The Bill will give legal recognition to transsexual people in their acquired gender. A person's gender will, subject to the issue of a full gender recognition certificate, become the acquired gender.
The Government's understanding of transsexualism is rightly founded on the Chief Medical Officer's recognition of gender dysphoria as a medical condition that may require treatment. Treatment has been available within the NHS for a considerable time.
The Government have discussed the aims, objectives and impact of the Bill with, among others, the British Medical Association, the General Medical Council, the Royal College of General Practitioners, the Royal College of Psychiatrists and the British Psychological Society.
The principle of legal recognition in the acquired gender is that a person's gender will, subsequent to the issue of a gender recognition certificate, become the acquired gender. That will ensure, on the whole, the continuing effect of gender-specific terms in legislative enactments. The Government have always intended that once a full gender recognition certificate is issued to an applicant, the person's gender becomes for all purposes the acquired gender. If the acquired gender is the male gender, the person's sex becomes that of a man, and, if it is the female gender, the person's sex becomes that of a woman.
Where under any legislation it is necessary to decide the sex of a person who has an acquired gender, or to say whether that person is man or woman, or male or female, the question must be answered in accordance with the person's acquired gender.
The Government, and the European Court of Human Rights, have always acknowledged that opinion is divided in some parts of the medical profession on the nature and cause of transsexualism. However, the Government support the position of the European Court of Human rights that the remaining controversy over the nature and aetiology of transsexualism must no longer stand in the way of transsexual people enjoying their basic human rights. That is the central and essential position that we take."