There is "no suggestion that Mark Harper knowingly employed an illegal immigrant", Downing Street have said.
The Immigration Minister has announced his resigned over the issue.
Number 10 said David Cameron had "accepted his resignation with regret".
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Detectives are investigating whether a 30-year-old man in Taunton died after taking 'spice', Avon and Somerset Police said.
Morgan Ackerman, 16, was playing "knock, knock ginger" with two friends when he ran out into the road and into the path of a taxi.