Calls for Mrs May to quit have grown louder since the resignation of border force chief Brodie Clark, whom she claims acted without Ministerial approval when checks were eased on visitors entering the UK.
Mr Clark, one of three officers suspended over the affair, has strenuously denied Mrs May’s claims, accusing her of misleading Parliament and suggesting that she was blaming him for “political convenience”.
Former Home Secretary Jack Straw weighed into the row yesterday as Labour MPs renewed their attack on a Government policy which could have allowed an unknown number of foreign terrorists and criminals into the country.
Mr Straw said: “What a great shame that the Secretary of State has jumped impetuously to a conclusion without any proper evidence, without allowing others to respond to that.
“At the heart of this debate is the conduct of the Home Secretary and the level of Ministerial responsibility – both for competence in running the department and moral responsibility for what happens in that department.
“The whole system will seize up unless those who are lower down in the system believe those at the top have their confidence and are ready, when things go wrong, to take responsibility.”
Mr Straw said a Home Secretary had to ensure they took the majority of the staff in their department with them.
“What you don’t do,” he added, “and I’m sorry the Secretary of State has embarked on this, is go for what appears to me, whatever her personal motives, both a vindictive and punitive approach of hanging someone out to dry because it appears to her that would be a good way of saving her career.”
Labour leader Ed Miliband denounced the situation as “a complete fiasco”.
Mrs May has said she authorised piloting the easing of some border checks on European Union travellers over the summer, partly to reduce queues.
But she told the Commons Home Affairs Committee on Tuesday that Mr Clark had gone further by scrapping checks against a Home Office database of suspected terrorists and illegal immigrants.
Mr Clark disputed Mrs May’s statement in his resignation speech, saying they were “wrong” and denying that he “added additional measures, improperly, to the trial of our risk-based controls”.
The Home Secretary’s side of the story has been supported by the chief executive of the UK Border Agency, Rob Whiteman, who released a statement insisting Mr Clark had admitted going beyond Ministerial orders.
Mrs May also has the backing of David Cameron, who told MPs yesterday that he supported the decision to suspend Mr Clark.
The Prime Minister said Mrs May had been right to authorise the pilot scheme of targeted checks on people entering the UK from Europe, which meant an easing of controls on those thought to be low risk.
It had resulted in a 10 per cent increase in illegal immigrants being spotted, as well as a 48 per cent rise in forged documents and double the number of firearms being seized, Mr Cameron added.
Home Affairs Committee chairman Keith Vaz said Mrs May could be recalled to give evidence because her account was so different to Mr Clark’s.
Mr Clark is to give evidence to the committee next week.
Unanswered questions for May: Page 13.