In a statement on Thursday to the House of Commons, Smith said 6,653 people without the right to work in the UK have been granted SIA licences and there are question marks over a further 4,400, taking the total to 11,053.
She insisted though that a “significant proportion” of this second set may be able to prove they can work.
It is still not yet clear what the split is between those who are illegal immigrants, and those who are here legally but do not have the right to work.
Since July, the SIA has been checking the immigration status of the approximately 40,000 non-EU nationals who are license holders. Of these, 28,737 have proved they have the right to work, according to the Home Secretary.
When news broke of the problem at the beginning on November, the total number of licences affected was put at 5,000, but this has been revised upwards following investigation.
Smith told MPs that enforcement action was being taking, saying: “Visits to specific individuals and employers have already begun and swift action has been taken in those cases which merit it.
“A series of targeted enforcement operations will take place in the coming months with a view to prosecuting employers and removing or prosecuting individuals in the worst cases.”
Earlier this month it was revealed at the Home Affairs Select Committee that only 150 licences have so far been revoked. Recipients have 21 days to from receipt of a letter from the SIA to prove they have the right to work in the UK, then a further 21 days in which to appeal after their license has been revoked.
But speaking on Thursday, Smith said 409 licences had been revoked of those checked from before 2 July, and more than 10,000 letters “instituting revocation” had been sent.
Smith also stressed that the SIA licence was only designed to show an applicant had undergone training and criminal record checks and that it remained an employer’s responsibility to check whether an individual had a right to work in the UK.
The news of the revised estimate was greeted with horror by the Conservatives, with Shadow Home Secretary David Davis claiming there had been a “huge policy failure” in the Home Office and said explanations on how it had “gone so badly wrong” was needed.