Alexander Faludy, 15, with an IQ off the normal scale, would have been the youngest Cambridge University undergraduate since William Pitt the Younger, despite suffering severe dyslexia; he can write only two illegible words a minute and also suffers from dyspraxia, "clumsy child syndrome".
His family believed the local council should provide funds for his degree course.
But a High Court judge ruled yesterday that Portsmouth City Council was correct in deciding that it had no duty to assess Alexander for special education needs or to provide extra financial support for his degree in theology and history of art.
Alexander and his family, of Servant Road, Portsmouth, now fear that his university place could be threatened if they fail to win financial backing from other sources.
Alexander, the son of two teachers, had told the judge at a hearing that he planned to go to Peterhouse in October, but he needed special equipment to read books and write his essays.
But Portsmouth City Council has refused him any extra money as he was not at a local authority school. His parents sent him to Milton Abbey, a fee-paying boys' boarding school in Dorset, three years ago, because he was being bullied at his state school.
After the ruling the family's solicitor, Samantha Chambers, said the family was disappointed. "Now that the local education authority will not be financially supporting Alex in his placement he must try to secure funding for his course at Cambridge from other sources.
"It would be very sad if, after overcoming his very significant learning difficulties, his place at Cambridge could be threatened by lack of finances."
She said the family would now need to raise between pounds 5,000 and pounds 10,000 a year for Alexander's three-year course to pay for tuition, equipment and someone to help him.
The British Dyslexic Association said there was still a moral case for support to be made available to Alexander Faludy, and others like him. It called on the Government to back its rhetoric by setting educational targets for children with special needs.
The association's chief executive, Joanne Rule, said: "There is a simple moral case for Alexander Faludy to be given the support he needs to reach his full potential.
"Alexander is exceptional, a truly gifted child. But there are many other dyslexic children whose ordinary school careers are equally unhappy, stuck in lower-stream groups regardless of their ability and afraid of being bullied.
"The Government must signal its determination that schools have higher expectations of pupils with special educational needs by setting targets for their performance."