The Home Office has launched an investigation into claims that migrants who speak no English are able to buy documents showing that they have passed a supposedly "secure" language test.
The Daily Mail reported that secret filming at one examination centre in London showed the certificates - which are required by anyone wanting to remain in the UK permanently or to apply for British citizenship - were being sold for £500.
Immigration and Security Minister James Brokenshire told the Mail: "The Home Office takes any allegation of fraud extremely seriously and we have already begun a full investigation.
"We will take the strongest possible action against anyone who is found to have abused the rules - including the possibility of criminal prosecutions for fraud."
Ofqual, the examinations watchdog, was also said to be aware of the allegations and was seeking further information "as a matter of urgency".
The Mail said that it had carried out its investigation into the examination centre at Upton Park, east London, which is run by Learn Pass Succeed (LPS), following information from a whistleblower.
Uzwan Ghani, one of the directors of LPS, which has four branches in London, told the paper the problem was confined to the Upton Park branch and that it had suspended tests taken at the centre.
"I'm shocked that this has happened and am very concerned as to how it could have happened," he was quoted as saying.
"We are very thorough when it comes to checking IDs of candidates before they take the test, so I will have to investigate which of the centres the test was taken in and who the assessor was.
"I've been in the business for five years and I've never come across something like this and I would not allow it. It is wrong and ridiculous."
LPS could not be contacted for comment.