The Prime Minister was challenged in the Commons over a statement made by Stephen Parkinson, a senior figure in the Vote Leave campaign, about Shahmir Sanni.
In response, Ms May acknowledged that being outed could be “difficult” for some gay people “because of their family and circumstances”.
But, on the future of Mr Parkinson – now her political secretary – she insisted: “Any statements issued were personal statements.”
Two Labour MPs demanded tough action against Mr Parkinson, with one, Angela Eagle, telling the Prime Minister: “Sack him”. Ben Bradshaw, another former minister, asked how Mr Parkinson’s actions could be “remotely acceptable”, adding: “It is a disgrace. Do something.”
At the weekend, Mr Sanni claimed that Vote Leave used its links with another pro-Brexit group to get around the £7m spending limit imposed by the Electoral Commission in a way that was “totally illegal”.
Responding to the allegations, Mr Parkinson revealed that he had been in a relationship with Mr Sanni – the first time his sexuality had been revealed, Mr Sanni's lawyers then stated.
Chris Wylie, the Cambridge Analytica whistleblower who disclosed the Facebook data breach, said Mr Parkinson’s actions had put Mr Sanni's family in Pakistan in danger, forcing them to take measures for their own security.
“He was forced to come out to his mum in the middle of the night because No 10 decided it was appropriate to out somebody,” Mr Wylie told BBC Radio 4's Today programme.
Challenged in the Commons, Ms May said: “I of course recognise the importance of ensuring that we do recognise, for some, being outed as gay is difficult because of their family and circumstances
“What I want to see is a world where everybody is able to be confident in their sexuality and doesn’t have to worry about such things.”
When urged by Ms Eagle to dismiss her political secretary, she replied: “No, I’m sorry that is not what I should be doing. My political secretary does a very good job as my political secretary. And, as I have said, any statements that were made were personal statements.”
At the weekend, Mr Parkinson said he was “saddened” by the “factually incorrect and misleading” statements by Mr Sanni and his lawyers.
He said: “I cannot see how our relationship, which was ongoing at the time of the referendum and which is a material fact in the allegations being made, could have remained private once Shahmir decided to publicise his false claims in this way.”
In his response to the statement, Jeremy Corbyn has accused the Government of turning “wild claims and red lines” into “climbdowns and broken promises” in the Brexit talks.
“The Government wasted months and months dithering and posturing before accepting the inevitable,” said the Labour leader.
Ms May insisted the transition agreement reached with the EU at last week's summit represented significant progress, telling MPs: “It is not in our national interest to ask businesses to undertake two sets of changes.
“Whilst I recognise that not everyone will welcome the continuation of current trading terms for another 21 months, such an implementation period has been widely welcomed by British business because it is necessary if we are to minimise uncertainty and deliver a smooth and successful Brexit.”
She acknowledged there were still “key questions” to be resolved around the Irish border issue.
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