A suspect in the alleged Manchester terror plot was allowed to enter Britain last week, despite irregularities in his immigration papers.

Sources said that the Pakistani man was given an appointment by officials at Manchester airport to return for an immigration interview. He was arrested this week in an internet café in the Cheetham Hill area of the city.

The man is one of 12 picked up in raids rushed forward on Wednesday after the police officer with national responsibility for counter-terrorism inadvertently disclosed secret briefing papers to photographers in Downing Street. Assistant Commissioner Bob Quick resigned within 24 hours, apologising for compromising the highly sensitive operation. The document that he was carrying disclosed that ten of the suspects in the case were Pakistani citizens on student visas.

A police source said that the decision to admit the suspect at the airport had been “a shambles”. He added: “This man’s documents were all over the place. He was allowed to proceed on the basis that he had to come back for an appointment with immigration and show them correct documents. He was never going to do that. He was effectively left free to do whatever he wanted.”

But security sources have suggested that the suspect might have been allowed “to run” in the expectation that he would lead the authorities to other conspirators. Although the arrests were made by Greater Manchester Police’s counter-terrorism unit, the investigation was being led by MI5.

Pakistan’s cooperation is considered vital in the inquiry and Gordon Brown has telephoned President Zardari in Islamabad to discuss the case. No 10 said that the two leaders were “committed to work together” to address the common challenge of terrorism.

But Pakistani intelligence officials claimed that they were still awaiting details from Britain about the men detained. They denied claims that two men had been arrested in Pakistan.

The hunt for the alleged terror cell’s bomb factory is continuing, with forensic scientists examining ten properties in Liverpool and Manchester. It is understood that no firm evidence of bomb-making materials or equipment has yet been found, although a large amount of material is being tested.

Police are said to have carried out the arrests after intercepted coded e-mails, referring to dates in April, raised fears that an attack might be imminent. Suspects were seen by surveillance officers conducting what might have been reconnaissance missions in Manchester city centre.

One source said: “We had to move early to protect the public, but that left less time to monitor them. The key now is to find the bomb.” If explosives material cannot be found to link the men to a bomb plot, the case may hinge on what evidence can be recovered from the suspects’ computers.

The possibility that there could have been one cell in Manchester and one in Liverpool, told to identify different targets, is also being examined.

One of the suspects had been living in Liverpool for two years after entering on a student visa. This has raised concerns that the visa system may have been exploited by militant groups.

At Friday prayers in Manchester, imams urged worshippers to remain calm and support the police. Mohammed Shafiq, chief executive of the Manchester-based Ramadhan Foundation, a Muslim youth charity, said: “Most visitors are peaceful people who abhor terrorism and we should not tarnish all Pakistanis or Muslims because of the actions of a small minority.”

Phil Woolas, the Immigration Minister, rejected claims that Britain was failing to cooperate with Pakistan on checking applicants for student visas. He was reacting to an assertion by the Pakistani High Commissioner in London that Britain would not allow it to help to carry out background checks on applicants. The High Commissioner had said that Britain was not doing enough. Asked if there was a problem with the British system for student visas, Wajid Shamsul Hasan replied: “Yes. If they allow us to make inquiries first, we can help them. But the thing is they have their own regime that vets these people.”

Mr Woolas told The World at One on BBC Radio 4: “We work very closely with the Pakistan authorities; indeed we’ve been criticised for doing so. We do have systems of checking these people to the best of our ability.”

In 2001, 4,860 visas were issued to Pakistanis wanting to study here, a figure that rose to 10,600 in 2007, after the US introduced tougher rules.

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