Since 2009, 100 doctoral candidates have won scholarships sponsored by Mexico's National Council for Science and Technology (Conacyt) to Manchester's Faculty of Engineering and Physical Sciences.
Of these, 44 sat the ToeflITP (Test of English as a Foreign Language Institutional Testing Programme), which consists of 140 previously used multiple-choice questions. It is designed to help students practise for real Toeflassessments.
According to the website of the Educational Testing Service (ETS), which runs the test, "ToeflITP forms have been administered before and are not fully secure; they should hence neither be used for admission purposes, nor as substitutes for a Toeflscore".
The website adds that the ITP is a "cost-effective" way to assess English ability.
A university spokesman said that all students had face-to-face interviews with academic members of staff "in which the proposed research topic was discussed at length".
He said ToeflITP results had been accepted "mainly to allow students from a poor background the chance to apply for a scholarship to study at Manchester".
The university selected the students in conjunction with partners in Mexico, the spokesman added.
Manchester stopped using the test in March 2011 and all students must now have a minimum score of 6.5 or the equivalent in the International English Language Testing System. The number of poor students applying for the scholarship had fallen as a result, the spokesman said.
The TOEFL ITP is not on the UK Border Agency's list of approved secure English language tests. However, the university has not broken any visa rules because the UKBA allows universities to choose how to assess whether students have an "intermediate" level of English.