All students seeking qualified teacher status in England must pass the 45-minute tests. But the council is pushing for a review of the situation due to the high failure rates. More than a quarter of candidates failed the numeracy test this year in some universities.
The council, which represents 87 UK universities and colleges involved in teacher education, said it is 'madness' to risk losing good candidates at a time of teacher shortages.
'Everything you've worked for, all the debt you've gone into over the past four, six, eight years, could come to nothing, on the basis of one false answer on one of those tests,' said UCET chair Professor Mike Newby.
The National Association of Schoolmasters/Union of Women Teachers is in favour of scrapping the tests as a number of its student members have also complained.
'The present inflexible requirements mean some highly gifted teachers may be lost to the profession because of an unnecessary additional test,' said the union's general secretary Nigel de Gruchy.
He pointed to the example of a member in Lancashire who gave up a successful career in the civil service to train as a teacher.
'Last year she achieved an upper second-class honours degree in English, and was appointed to a post in a primary school. Inspectors have praised her work, but so far she has failed the numeracy test four times. If she fails again, she loses qualified status,' he said.