UK Border Force chief Brodie Clark stepped down on Tuesday saying Mrs May's claim that he had gone further than ministers authorised was "wrong".
MPs will debate the row later as Labour demand more details of Home Office guidance given to the UK Border Agency.
Labour's Yvette Cooper said the row was "sapping confidence" in Mrs May.
'Serious answers'Mrs May says that she had allowed some checks on European travellers to be relaxed for a four-month period from July, but said Mr Clark went further in scaling back checks - including on people from outside the European Economic Area - without her approval. He was suspended last week.
But in a statement released on Tuesday evening, Mr Clark stepped down, saying he would lodge a claim for constructive dismissal and that Mrs May's remarks had made his position "untenable".
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