Millions of landlords could be unwilling to rent property to immigrants if government proposals requiring them to carry out immigration checks are put into practice, an influential crossparty committee of MPs has warned.

The Commons home affairs committee says the measures – contained in the government's new immigration bill – are designed to create a hostile environment for illegal migrants. But it warns that the proposals will discriminate against all immigrants, regardless of their status.

The group of MPs also says it would be "wholly wrong" to introduce health charges to access the NHS for those who are in Britain through no choice of their own, such as refugees and the victims of trafficking.

The committee's chairman, Keith Vaz, said that the combination of the controversial immigration advertising vans, Capita's texts to British citizens asking them to leave the country and the U-turn on visa bonds added up to a "chaotic summer for immigration policy".

He said that if the government wanted to get tough on illegal immigrants it could take more seriously the allegations that people make over its hotline about those in Britain illegally.

"Currently only six in 100 reports of illegal immigrants result in an actual investigation and only 1.5 in 100 results in removal," said Vaz.

But the MPs reserve their strongest criticism for the requirement on millions of private landlords to carry out immigration checks on behalf of the Home Office, pointing out that there are more than 400 "legitimate European identity documents alone on which landlords will have to base their decision".

"There is a possibility that landlords will discriminate against all immigrants regardless of their status rather than take the risk of housing a person without right to remain," say the MPs, adding that an official impact assessment is needed to gauge its effect on discrimination against migrants.

They point out that four years ago the then attorney-general, Lady Scotland, was fined £5,000 for unknowingly employing an illegal immigrant.

"If one of the government's law officers can make such a mistake, it would be very easy for the average citizen to do so," they say, pointing out that "the vast majority of private landlords are private individuals, most of whom let a single dwelling".

They also warn that some unscrupulous landlords will hold to ransom tenants who are suspected of being an illegal migrant and drive more people into the twilight world of "beds-in-sheds" and overcrowded houses.

Liberal Democrat concerns about the plan have already led to a commitment that the scheme implementation will be limited to a pilot scheme in one part of the country this side of the general election, but Labour has already pressed for that to be expanded.

The committee's last quarterly report on the work of the UK Border Agency says there were still 432,000 cases in its backlog when it was wound up in April. The MPs say that a reduction of 70,400 in the backlog had only been achieved by simply loading pending cases onto the computer and, in some categories, such as those applying for further leave to remain on the basis of marriage or civil partnership, the backlog had actually grown.

The committee say they are not opposed in principle to introducing NHS charges for those who are in Britain temporarily to work, study or visit but say it would be "wholly wrong" to charge those who are here through no choice of their own such as victims of trafficking, refugees, or other vulnerable people. They suggest a system under which visa applicants are required to take out private health insurance instead.