Employers who exploit immigrants by offering them lower wages and worse conditions than British residents could be jailed under a Labour government, Ed Miliband will say on Monday.

In a speech in Norfolk, the Labour leader will commit to introducing a law dealing with the poor working conditions of many migrants and the resulting downward pressure on wages for local workers.

Labour cited one case that police felt unable to prosecute under current laws, in which 29 immigrants claimed to have had their wages stolen and to be living with up to 12 people crammed into a two-bedroom house with bedbug-ridden mattresses. They also claimed to have been beaten, set upon by dogs and held in the back of a van for up to six days at a time.

“We are serving notice on employers who bring workers here under duress or on false terms and pay them significantly lower wages, with worse terms and conditions,” Miliband will say.

“This new criminal offence will provide protection to everyone. It will help ensure that when immigrants work here they do not face exploitation themselves and rogue employers are stopped from undercutting the terms and conditions of everyone else.”

The Labour leader is to speak in the Conservative-held Norfolk marginal of Great Yarmouth, which Labour lost in 2010 and which has since been identified as a Ukip-friendly seat. Miliband will warn that neither the Tories nor Ukip are prepared to tackle the root causes of concern about immigration. “They turn a blind eye to exploitation and undercutting because it is part of the low-skill, low-wage, fast-buck economy they think Britain needs to succeed,” he will say.

Despite Miliband’s speech directly addressing immigration, there were reports on Sunday night that Labour MPs have been given a strategy document suggesting they should “move the conversation on” if voters express concerns about border controls.

Labour aides dismissed the quotes as being taken out of context from a lengthy document about how to tackle the threat of Ukip but the Telegraph reported the document urges them not to send leaflets on immigration to all voters because it could be “unhelpful” and “risks undermining the broad coalition of support we need to return to government”.

Labour’s proposed law is based on German legislation which states that anyone who “exploits another person’s predicament or helplessness arising from being in a foreign country to subject them to slavery, servitude or bonded labour, or makes him work for him or a third person under working conditions that are in clear discrepancy to those of other workers performing the same or a similar activity, shall be liable to imprisonment from six months to 10 years”.

To prove that a criminal offence has been committed, evidence would have to be provided that an abuse of power has occurred and that migrants were employed on significantly different terms to local workers. Undercutting of wages and conditions would not constitute a criminal offence but could be used as evidence of exploitation.

Immigration from EU member states has become a significant issue since the rise of Ukip, with both Labour and the Tories now promising to crack down on benefits for new arrivals. On Sunday night, a OnePoll survey for ITV found 42% of voters wanted to leave the EU while 31% wanted to stay in, although many were undecided. It also found 60% would like a cap on EU immigrants and 23% wanted an outright ban.

Miliband has been addressing the issue of immigration head-on in recent months in the face of a growing threat from Ukip to his party as well as the Conservatives. He has promised to listen to people’s concerns about immigration without stooping to the rightwing rhetoric of both those parties.

Some of Labour’s existing policies include increasing the fines for firms paying below the minimum wage, closing down loopholes in agency worker laws that allow firms to undercut directly employed staff, and banning recruitment agencies from hiring only from abroad.

On Sunday Yvette Cooper, the shadow home secretary, said Labour would introduce measures to stop foreign criminals getting British passports by requiring applicants for citizenship to produce criminal record checks from their home country to help prevent abuse.

This week John Vine, the chief inspector for borders and immigration, disclosed a case from 2013 in which an applicant revealed they had stabbed someone to death before fleeing to the UK but the Home Office was unaware and granted citizenship anyway.

Cooper said: “I think it’s shocking that we have had people including serious criminals and killers given British passports and British citizenship because the Home Office failed to do basic checks.”

She also called for an investigation into allegations of sexual assault against detainees at Yarl’s Wood immigration detention centre, following reports that male staff had attacked women being held there.