Thousands of foreign students remain unaccounted for after the Home Office showed a lack of urgency in tracing them, according to an inspection report.
The immigration watchdog warned last year that there was no process in place to monitor individuals in a category which had more than 70,000 cases, meaning the number who have stayed in the country illegally was unknown.
The figure has been reduced since the issue was first highlighted by the Chief Inspector of Borders and Immigration David Bolt.
But following a re-inspection, it emerged that around 16,000 overseas nationals have still not been located by immigration authorities.
Mr Bolt acknowledged that "data matching and cleansing" has substantially reduced the figure.
However, his assessment said there had been no directly related enforcement activity, adding: "I believe that the Home Office's approach has lacked urgency, a view that the Home Office strongly disputes.
"The Home Office's case would be helped if it were to set a clear timescale for the completion of this work."
The latest findings relate to the system for cutting short the stay in the UK of those who come to the country for study purposes.
Students from outside Europe must apply under tier four of the points-based visa system and produce a form from a licensed education establishment which acts as their sponsor.
Sponsors must notify officials of any changes in a student's circumstances that would affect their sponsorship, such as failure to enrol on their course, a pattern of unauthorised absences, withdrawal or expulsion, or early completion of their studies.
Once notified, officials consider the case and decide whether to curtail the student's leave to stay in the UK.
Mr Bolt's original report, which was published in March last year, identified cases where curtailment was not pursued (CNP) as being "of most concern".
These include those who had a period of leave remaining that was shorter than the time they would be permitted to wrap up their stay and depart, plus those who had already overstayed.
Many of the 71,601 CNP decisions recorded in the two years to April 2015 may have departed the UK or been granted leave to remain on other grounds, but the true position was not known, the initial review said.
The latest report also highlighted the size of the "work in progress" caseload, with nearly 25,000 tier four curtailment notifications waiting to be considered.
Mr Bolt raised concerns about "severely scaled back" resources allocated to the work.
Inspectors found during an on-site visit in January that there were two members of staff working on tier four curtailments and two more dedicated to complex cases.
Separate reports from the watchdog published this week flagged up "poor" coverage of unmanned sea ports and warned that Border Force's operations at Gatwick airport have come under "considerable strain".
In a response to the report on tier four curtailment, the Home Office said the number of outstanding cases has been halved since the time of the re-inspection after additional resources were deployed.
On CNP cases specifically, the department acknowledged there was more work to do, but emphasised the importance of "working through this cohort methodically and comprehensively to avoid unnecessarily pursuing enforcement action against those that have left the UK or remain in the UK lawfully".
It said the number unaccounted for has been reduced to approximately 16,000, adding: "We are now pursuing phase two of this work which will involve using external databases to identify those within this cohort who have remained in the UK unlawfully and will be passing results onto enforcement colleagues for consideration."
A Home Office spokesman said it had made "significant progress" against recommendations in the previous report.