The scheme was introduced by Ministers as part of attempts to create a “hostile environment” for those in the UK unlawfully.
It requires banks and building societies to check the immigration status of all current account holders against details of known illegal migrants held by authorities.
Where an illegal migrant is found to be operating an account, this will be flagged to the Home Office.
After checks, officials will instruct the bank or building society on what action to take, which could include shutting the account.
Campaigners have criticised the move, with concerns that mistakes could be made while the Home Office determines people’s immigration status
Immigration Minister Caroline Nokes said: “These new measures are part of our commitment to make it more difficult for people with no right to live or work in the UK to remain here.
“This will not affect those who are in the UK legally but we must be firm with those who break the rules as illegal immigration impacts the whole of society.
“Those living and working in the UK illegally can drive down the wages of lawful workers, allow rogue employers to undercut legitimate businesses and put pressure on taxpayer-funded public services.
“By tackling abuse in this way, we can build an immigration system which works in the best interests of the country and prevents vulnerable people from finding themselves at risk of exploitation.”
The Home Office said it was only sharing details of illegal migrants who are liable for deportation from the UK, or who have absconded from immigration control.
Those with outstanding applications or appeals will not be affected – including asylum seekers – nor will those who have been granted leave to be in the UK, including refugees, the department added.
But campaigners criticised the measures.
Chai Patel, legal policy director of the Joint Council for the Welfare of Immigrants, claimed the Home Office frequently makes mistakes determining immigration status.
He added: “What is shocking about this system is that people’s bank accounts, which they rely on for their jobs, their homes, and every aspect of life, can be closed with no clear means of redress or compensation in case of errors.
“Additionally, this places people affected at even greater risk of exploitation and of being driven into a cash-only economy at the mercy of unscrupulous employers and landlords.”
A spokesman for trade association UK Finance said: “As a legal requirement implemented by Government, banks and building societies are now required to review the immigration status of all existing customers and have a duty to inform the Home Office when they identify a person without leave to remain in the UK from holding a current account.
“This is an extension to existing rules introduced in 2014 which require banks and building societies to conduct a check on a person’s immigration status before opening a current account for them.”