The students can stay on for two years after graduating
Rules allowing non-European students to stay in the UK after attending further education colleges should be reviewed, a government advisory panel says.
The Migration Advisory Committee says it is concerned students can obtain two-year visas regardless of the standard of the teaching or degree.
The rules form part of the points-based scheme to attract and retain highly-qualified and skilled workers.
The government said it would consider the MAC report's findings.
Immigration minister Phil Woolas said: "The points-based system is a powerful and flexible tool which means that businesses can recruit the skilled foreign workers that the economy needs, but not at the expense of British workers, nor as a cheaper alternative to investing in the skills of the existing workforce."
In the last academic year, 42,000 students from outside the European Economic Area obtained the visas to stay on after obtaining a degree.
They were granted under the Post-Study Work Route, part of Tier 1 of the points-based system, aimed at "highly skilled" migrants.
MAC head David Metcalf said he was "amazed" and "staggered" that 599 of the institutions which issued degrees were not "proper" universities.
"They are basically further education colleges which get their degrees validated by one of the universities," he said.
"What we think is, without being overly elitist, is that we should have a good look at these institutions to see if it is legitimate for all the students studying there on all the courses to get post-study work visas."
A survey for the UK Border Agency of 1,564 graduates given the visas found about half worked in professional occupations, and "significant" numbers were in less skilled employment.
But Prof Metcalf said there was no evidence the foreign students were taking jobs from British students.
MAC's report suggested foreign students could be forced to find a job within several months of finishing their course before they are given a full two-year visa.
However, it noted that changing the system could impact on colleges which rely on foreign student fees and create an "Ivy League" of institutions that would come with visa entitlements.
Shadow immigration minister Damian Green said the report was "late recognition of the chaos surrounding student visas... one of the most significant loopholes in our immigration system".
Liberal Democrat home affairs spokesman Chris Huhne welcomed a crackdown on institutions exploiting immigration loopholes but said any reform should consider the effect on the industry.