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In a statement issued on his behalf, it was announced that he would step down from today.
Housing Minister Phil Twyford's office said he would not be commenting on Mr Barclay's resignation as it was an employment matter.
Last month, Mr Twyford confirmed that Mr Barclay had not been at work for a number of weeks.
The absence was due to an employment dispute, but the minister did not go into further details at that time.
At the time the ministry issued a statement saying Mr Barclay had not quit, despite speculation.