But now, to the fury of the exams’ designers, companies are offering to coach sixth-formers through a new set of admissions tests to Oxford, Cambridge and other top universities, at up to pound;300 per student.

The development, which raises the prospect that those able to afford the coaching will gain an advantage in the tests, is creating a new row in the continuing controversy over attempts to widen access to higher education.

From this year, UK students wanting to study law at any of the eight leading universities have to take the National Admissions Test for Law, a two-hour exam involving 24 multiple-choice questions and an essay. Students applying to read medicine at Oxford, Cambridge and three other universities are also faced with the BioMedical Admissions Test, a 90-minute exam of 50 multiple-choice questions.

Both have been introduced as admissions tutors struggle to distinguish between sixth-formers with many A-level A grades. Both websites for the tests say that students should not bother paying for expensive tuition, and offer free practice tests themselves.

However, at least three firms are running coaching courses for the BMAT medicine tests, while two are offering them for LNAT, the law test. Kaplan Test Preparation and Admissions, which claims to offer “the UK’s first ever preparatory courses” for the tests, offers five hours’ tutoring in either for pound;300, or a course of four three-hour lessons to be taken with other students for pound;199.

Bene’t Steinberg, a spokesman for the University of Cambridge Local Examinations Syndicate, which designed the BMAT test, said: “We would urge people not to waste their money on very expensive courses.”

However, Louise Cook, centre director for Kaplan in London, said: “We have been preparing people for tests such as these for 70 years. We are confident that we can help students perform to their very best.”