However, to avoid discriminating against people on grounds of "race and ethnicity", everyone who rents a property will be required to provide their passport or other proof of their right to live in Britain.
Landlords will be required to assess whether they think immigration documents provided to them are forgeries. If so, they will be expected to contact the Home Office to raise their concerns.
When the scheme was first proposed in the Queen's speech, Eric Pickles, the communities secretary, privately raised concerns that it would "inflict red tape on millions of people"
He is understood to have suggested that it should be limited to high risk areas so that it did not have a "disproportionate" effect on people.
However, the measures unveiled yesterday by Theresa May, the Home Secretary, were significantly more far-reaching.
The consultation document states: "Landlords must make checks on a non-discriminatory basis, i.e. they should not make any assumptions about a person’s migration status based on their ethnicity, name, accent, etc."
The move would effect all 4million people who rent homes in Britain. UK citizens would be required to provide a copy of their passport when they sign new tenancy agreements.
Those from outside the European Economic Area would be required to supply their residence permit or visa stamp.
The consultation document suggests that the move would affect 1.4million private landlords.
Under the proposals, private landlords would have to carry out checks on the migration status of every tenant before renting out a room.
Those who failed to do so would be fined £1,000 for every illegal immigrant in their property, while those previously sent an advisory letter warning them about failing to make proper checks faced fines of £3,000 per tenant.
The Home Office consultation said: "If a person cannot produce satisfactory evidence, the landlord should not rent accommodation to them."
However the National Landlords Association raised concerns about the burden the plans would put on landlords.
A spokesman said: "If this is to work, it is vital that the system is simple, straightforward and easy for landlords to use and understand.
"It makes sense to base the requirements on the established system used by employers to verify that individuals have the right to work in the UK, not least because there is a clear acknowledgement that employers, like landlords, are not immigration experts.
"They can only be expected to carry out reasonable checks that someone is who they say they are, and that they have the documentation to prove they have the right to be here."
The rules would not apply to university halls of residences, boarding schools, children's homes and homeless hostels.
Theresa May, the Home Secretary, said: "We will not allow the growth of a shadow economy for illegal migrants whether it is in employment or housing.
"The new regulations will make it more difficult for illegal migrants to find accommodation and deter those who set out to disregard the Immigration Rules. It will benefit those communities blighted by illegal structures, the so called 'sheds with beds'."