A company which provides staff to clean government buildings launched a probe after it sent five illegal immigrants to work in a Home Office premises.
The news will put more pressure on Mr Reid
The Nigerians were arrested in London after being sent to the Immigration and Nationality Directorate's Becket House.
Earlier this week a director at the IND caused a row after saying he did not have the "faintest idea" how many illegal immigrants were in the UK.
Techclean said the five men appeared to have "circumvented" safeguards.
"Techclean PLC and its subsidiaries have in place recruitment procedures in strict accordance with government guidelines and take the process of recruitment extremely seriously," the company's statement said.
"We are conducting an internal enquiry into a case where five employees appear to have circumvented these safeguards.
"This matter is subject to investigation and we will not be making any further statement at this time."
Home Secretary John Reid, who has come under fire after also admitting he had no idea of how many illegal immigrants were in the UK, said the Home Office would not use the firm again until it had better vetting procedures in place.
He said the additional vigilance of a security guard helped identify them.
The Home Office said: "These individuals were the employees of a firm contracted to provide cleaning services.
"It is policy that all employees and contracted employees working in Immigration and Nationality Directorate (IND) buildings have security and employment checks carried out, which include checks on their immigration status.
"Of course we will investigate further and appropriate action will be taken as necessary."
Shadow Minister for Immigration, Damian Green MP, said the news sparked "more questions than it answers".
"How long have they been using this firm? Do other government departments use the firm? How confident is the Home Office that previous cleaners supplied by the firm were not also illegal?" he said.
Liberal Democrat Shadow Home Secretary, Nick Clegg MP said the Home Office appeared "woefully under prepared" in dealing with illegal immigrants.
"If even the Home Office is having trouble identifying illegal immigrants in its own buildings, it is no wonder other businesses are struggling," he said.
Earlier this week the IND's director of enforcement and removals, Dave Roberts, caused a row after conceding he did not have the "faintest idea" how many illegal immigrants were in Britain.
He told the Commons home affairs committee those who overstayed their visas were not pursued individually. The strategy was to target larger groups of failed asylum seekers working for the same employer.
Later this year new laws will come into force making companies liable for fines of up £2,000 per employee given work when the employer knew it was against the law.
Mr Roberts told MPs: "We are making huge efforts to remove them but not at the basis of tracing individuals."
Immigration minister Tony McNulty said on Wednesday the best estimate for the number of illegal immigrants was between 310,000 and 570,000. Removals ran to about 25,000 a year.