The backlog of 153,000 notifications could potentially have meant that thousands were wrongly allowed to remain in the country, the Chief Inspector of Borders and Immigration said.
The tip-offs were all reviewed by May this year, but Mr Vine said it must be an "ongoing priority" to make sure checks are carried out.
His team examined work at three UKBA offices in Sheffield, Beijing and Delhi.
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Official statistics show there were 82,694 inmates in jails in England and Wales on Friday.
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