I have seen an article from am immigration lawyer. This paragraph really caught my eye.
Banks will be required to check bank accounts against a database of people in the UK illegally, yet a further instance of the Home Office outsourcing immigration control by placing the burden on the private sector.
Why rely on the banks, The Home Office has a list of immigrants that have overstayed their visa. I know of one person on an overstayed visa that is working with a National Insurance Number , and has even had 3 National Health stays in the last two years. The Department of Works and Pensions issues National Insurance Numbers, surely its not to hard for these two departments to syncronise their data banks and identify, the illegal immigrants that have overstayed their visas.