The home secretary is to appear in the Commons following claims hundreds of thousands of people were allowed to enter the UK over the summer without proper security checks.
Mrs May is facing Labour demands to disclose whether any terror suspects are believed to have entered the country after border guards were instructed not to carry out certain passport checks.
The head of the UK border force, Brodie Clark, has been suspended and an inquiry set up under John Vine, chief inspector of the UK Border Agency.
But Shadow Home Secretary Yvette Cooper insisted that urgent steps were needed to establish whether the public was at risk.
In a letter to Ms May, she said: "The first, and crucial, step must be to ascertain the implications of the lapses in security and passport checks.
As far as our staff were concerned, this was all done with ministerial authority Sue Smith
"In particular we need to know whether anyone posing a threat to Britain's national security was allowed to enter the UK during the period where the decision of ministers to relax passport checks was taken further than the Home Office has said was ordered."
Ms Cooper said the public were "understandably appalled and shocked" at the reported failings at the UK Border Agency and urged that Mr Vine's inquiry be "all-encompassing", covering the Home Office, ministerial decision-making and cuts to staff numbers.
Done with ministerial authority?
The Public and Commercial Services Union (PCS) has claimed that border controls were relaxed to keep queues down despite cuts to personnel. It also said the decision was authorised by ministers.
Ms May is due to make a statement to the Commons later. According to reports, border guards were told this summer not to bother checking biometric chips on the passports of citizens from outside the European Union to ensure they are not fraudsters.
The guards were also instructed not to bother checking fingerprints and other personal details against a Home Office database of terror suspects and illegal immigrants, it was claimed.
Sue Smith, of the PCS, blamed what she claimed had been a 10 per cent reduction in border force staff.
"The travelling public understandably want to have a fast and efficient service, and yet we are also under a reduced workforce," she said.
"So, I think senior managers have seen this as a way to provide the public with what they want."
She added that senior managers had told the union that the changes to border checks had been made with the authorisation of ministers.
"As far as our staff were concerned, this was all done with ministerial authority, and that's the information we have received," she said.
05 November 2011