The Liberal Democrats are trying to kill off the government's "right to rent" plans which force landlords to assess the visa status of migrant tenants and which, critics claim, will fuel racism akin to the dark days of "no dogs, no blacks, no Irish" signs on doors.

Under right to rent, landlords must check the immigration status of tenants to make sure they are legally allowed to be in England and report those who are not to the Home Office. Landlords breaking the rules face fines of up to £3,000. The Home Office said it will make it harder for illegal immigrants to stay in the country and easier to tackle the rogue landlords who house them.

The changes were brought in under the Immigration Act 2014 and trialled in the West Midlands. Now the government plans to roll out right to rent across the whole of England. But critics say the scheme encourages England's 1.8 million landlords to racially discriminate against potential tenants.

"These plans are trying to turn landlords into free labour for the immigration service," said Lib Dem leader Tim Farron. "But more than that it is the worst kind of ineffectual, dog whistle politics that this government has become synonymous with. The Liberal Democrats in both the House of Commons and Lords have tabled motions to try and kill this plan outright."

The Joint Council for the Welfare of Immigrants, a charity, says its research shows "in the first six months, the 'right to rent' checks had resulted in discrimination against people with foreign accents, foreign names and those without British passports".

But an evaluation by the Home Office of its pilot in the West Midlands found "no evidence" that those from minority groups were less likely to secure a tenancy than white people. It did, however, note those from ethnic minorities were more likely to be asked for documentation and "comments from a small number of landlords ... did indicate a potential for discrimination".

A Home Office spokesman said right to rent "is part of the government's approach to building a fairer and more effective immigration system".

"It will deter people from staying in the UK when they have no right to do so, while having no adverse effects on those who do have the right to live here," he said. "We continue to work closely with the expert panel, including representatives from housing and homelessness charities, that helped design a list of acceptable documents for a whole range of scenarios, including where British citizens do not have a passport."

Labour has also been critical of right to rent. Shadow home secretary Andy Burnham wrote in the Independent on Sunday that right to rent "in its current form could lead to widespread discrimination".

"Of course, we have come a long way as a society since landlords displayed unwelcoming notices in their windows," he wrote. "But the new document checks could become the modern equivalent of the 'no dogs, no blacks, no Irish' signs and, by being more insidious, such casual discrimination will be far harder to challenge."