Home secretary defends proposals in Thursday's flagship bill following claims that they will be unfair and unworkable

The home secretary, Theresa May, has defended plans to create a "hostile environment" for illegal migrants to Britain, as immigration lawyers warned her that a system of identity checks for all, including British citizens, would have to be introduced to enforce the government's moves to curb access to privately rented housing and to tackle alleged health tourists.

The warnings come as she publishes her flagship immigration bill on Thursday, which will require immigration checks to be carried out before anyone can open a new bank account, be issued with a driving licence or access routine health treatment.

Speaking on BBC Radio 4's Today programme, May said: "Most people will say it can't be fair for people who have no right to be here in the UK to continue to exist as everybody else does with bank accounts, with driving licences and with access to rented accommodation. We are going to be changing that because we don't think that is fair."

The Home Office bill will include measures spanning six other Whitehall departments including justice, transport, business, health, local government, and work and pensions, and is designed, in May's words, to "create a really hostile environment for illegal migrants". "What we don't want is a situation where people think that they can come here and overstay because they're able to access everything they need," May has said.

The Home Office confirmed the bill would:

• Require private landlords to check the immigration status of their tenants.

• Require temporary migrants, such as overseas students, who have only a "time-limited" immigration status, to make a contribution to the NHS. A £200 levy has been mentioned as an option.

• Require banks to check against a database of known immigration offenders before opening a bank account.

• Create new powers to check the immigration status of driving licence applicants and to revoke the licences of overstayers.

• Introduce a "deport first, appeal later" policy for thousands facing removal who face no "risk of serious irreversible harm" from being sent back, and reduce the grounds for appeal from 17 to four.

On Today, May declined to give any estimate of the scale of "health tourism" in Britain but confirmed the bill included a health levy on overseas students and other categories of short-term migrants. She gave no figure for the levy and said the Department of Health would publish detailed proposals in the next few weeks. She denied it would cost more to collect the levy than the amount it raises.

"We will be asking for a surcharge; there will be a sort of levy on people who are going to be coming here, to be staying for a while, to contribute so people can feel it is fair," she told the BBC. "One of the things the NHS has always been quite bad at is charging people who they should be charging, people who don't have the right to free access to the NHS and recovering those costs from them."

May did not spell out how the identity checks to establish the immigration status of those applying for health treatment, housing, bank accounts or driving licences would be carried out. But she did say that private landlords would have access to a helpline similar to that currently used by employers to help them carry out the checks.

The bill will also restrict the ability of immigration detainees to apply repeatedly for bail if they have already been refused it and create stronger guidance for the courts on the use of human rights laws to prevent deportation, particularly the right to family life.

There are also plans to make it easier for the Home Office to recover unpaid fines from companies who employ illegal migrants, and local authorities may face fines for letting social housing to tenants without a direct connection to a local area.

However, leading lawyers, landlords, immigration welfare charities and housing organisations have warned that the bill will lead to a real risk of increased homelessness, including of families, and widespread discrimination.

The Immigration Law Practitioners' Association (Ilpa) has told May her plan for millions of private landlords to face "proportionate" fines of up to £3,000 if they fail to conduct checks on the immigration status of new tenants and other adults living in their properties is unworkable.

The lawyers say the combination of the new housing and health checks with existing checks carried out by employers and educational colleges amounts to a system of identity checks for foreign nationals in Britain.

"What this means in practice is a system of identity checks for all, since it is necessary for British citizens or people with permanent residence to prove that they are lawfully present in the UK if and when checked," says the immigration lawyers' official response to the Home Office consultation.

"British citizens, European economic area nationals and third country nationals alike would be required to produce identity documents at many turns in a scheme that would be intrusive, bullying, ineffective and expensive and likely racist and unlawful to boot," says the Ilpa response.

The lawyers say the scheme is discriminatory because landlords are likely simply to say they aren't satisfied with a tenant's identity documents and refuse them accommodation. They also point out that somebody's immigration status is not necessarily straightforward, with the proposals taking no account of those who do not yet have leave to remain in Britain but have an outstanding application that clearly meets the immigration rules.

The Residential Landlords Association has told the home secretary that there are potentially 404 types of European identity documents that landlords may need to know about to operate the scheme. They also warn that some landlords will simply refuse to house migrants for fear of falling foul of the new rules.

Habib Rahman, of the Joint Council for the Welfare of Immigrants, predicted that "these measures will divide society, creating a two-tier Britain, a return to the days of 'no dogs, no blacks, no Irish' and of ill people with no access to healthcare walking the streets of Britain. This bill is a travesty and must be stopped."

But the immigration minister, Mark Harper, defended the bill, saying it would "stop migrants using public services to which they are not entitled, reduce the pull factors which encourage people to come to the UK and make it easier to remove people who should not be here".