Home Secretary Theresa May has admitted she does not know how many people came into the UK without proper checks.
An inquiry has been ordered into claims identity checks on travellers from outside Europe were scaled back in the summer, without ministerial approval.
In a statement to MPs, Mrs May said those responsible would be punished. Brodie Clark, head of the UK border force, is among three staff suspended.
Labour accused Mrs May of giving "the green light for weaker controls".
No 10 has said Mrs May has the "full confidence" of the PM.
Mrs May told the Commons that while ministers had started a pilot project "targeting intelligence-led checks on higher-risk" passengers, Mr Clark had "authorised the wider relaxation of border controls without ministerial sanction".
She said: "As a result of these unauthorised actions, we will never know how many people entered the country who should have been prevented from doing so after being flagged by the warnings index."
She added that staff at the UKBA had been "let down" by senior officials at the head of the organisation, who had put border security at risk.
Under the pilot scheme which began in July, Mrs May said, checks were relaxed on European children travelling with their parents or school who were not considered a credible risk.
Under limited circumstances, officials could also use their discretion on whether to open biometric chips on passports to check the second secure photograph.
However, she said biometric checks on European nationals and warnings index checks on children from the EU "were abandoned on a regular basis, without ministerial approval".
Mrs May added that adults were not checked against the warnings index at Calais, and also said that fingerprinting of non-EEA nationals from countries that required a visa was stopped, again without ministerial approval.
"I did not give my consent or authorisation for any of these decisions," Mrs May told MPs.
"Indeed I told officials explicitly that the pilot was to go no further than we had agreed."
Shadow home secretary Yvette Cooper said: "The truth is that instead of strengthening the checks year on year, as all previous ministers had committed to do, this home secretary decided to water them down as official government policy, even though she never told this House.
"She has blamed officials for relaxing the checks further than she intended. But she gave the green light for weaker controls."
She accused Mrs May of presiding over "growing chaos and corner-cutting at our borders".
"Thousands of people have entered without proper checks and without the home secretary having a clue what was going on," she added.
The BBC's Tom Symonds said the question was now whether border agency staff had misinterpreted the home secretary or intentionally gone further to reduce queues and pressure on the agency.
Earlier, Ms Cooper said in a letter to Mrs May that the independent inquiry should have a wide-enough remit to fully investigate "the actions of the Home Office, ministers and the effect of resource cuts on UKBA decision-making".
Mrs May announced there would be three inquiries, the main one led by the Chief Inspector of the UK Border Agency, John Vine.
On Tuesday, Mrs May will face questions from the Home Affairs Select Committee, in what was a previously arranged appearance.
Its chairman, Keith Vaz, said he wanted to know whether the pilot scheme was monitored and whether immigration ministers had met with senior UKBA officials during the scheme.
"We need to know this agency is fit for purpose," he said.
Lucy Moreton, from the Immigration Services Union (ISU), told BBC Radio 4's Today programme staff "were not aware that the minister did not know" about checks being relaxed.
"As far as staff were aware, this had been ministerially sanctioned," she said.
"It's a requirement. We aren't allowed to make that decision ourselves to relax those checks."
Noting that Mrs May says she was unaware of the practice, Ms Moreton added it was "entirely possible" that Mr Clark or someone else at that level made the decision themselves.
Labour and unions have claimed that staff shortages - due to cuts to the UKBA - are at the root of the problems.
Some 5,000 posts are due to go by 2015 as part of wider government cost-saving measures.
Ms Moreton said that although every passenger coming into the UK was supposed to be seen by an immigration officer, "there are instances where there are not enough staff" to cover certain planes or freight traffic.
"It's not supposed to happen, and often it doesn't happen on purpose, but it does happen," she said.