Prime minister wants migrants to prove they have been continuously looking for work in order to receive income benefits

The political rhetoric over immigration will further intensify on Monday as David Cameron promises to ban all EU nationals from claiming most benefits after six months in the UK unless they can prove they have been continuously looking for work over that period.

The proposal does not go as far as banning EU migrants access to income-related benefits entirely for the first year in the UK, as had previously been suggested. However, the proposal may still put the UK at odds with the EU over restrictions on free movement of workers.

Cameron will also set out plans to restrict foreigners from access to social housing if they have not been resident in the UK for five years, plans widely trailed over the weekend, as well as making it easier for the NHS to claim back the costs of treating people from overseas.

In a speech setting out the government package to deter so-called benefit tourism, Cameron will say EU migrants can only continue to claim jobseekers allowance if they have been continuously actively seeking work and have a realistic imminent prospect of finding a job.

Cameron will say he wants to "create a system that is fair so that we support the aspirations of hard-working people who want to get on in life. Ending the something for nothing culture needs to apply to immigration as well as welfare. We're going to give migrants from the European Economic Area a very clear message. Just like British citizens, there is no absolute right to unemployment benefit."

Figures on numbers of non-UK nationals claiming out of work benefits are shaky. But in January 2012, the Department for Work and Pensions said that 371,000 people claiming working-age benefits were non-UK nationals when they first applied for a national insurance number. Among that number, 258,000 were non-EEA nationals.

All three main party leaders have been offering varied packages to address voters' concerns about migrants, and the perception that they are taking jobs or have privileged access to public services.

At the weekend Nigel Farage, the Ukip leader, predicted that his commitment to end EU citizens' automatic right to work in the UK would be the chief source of his party's future popularity.

Although the Bishop of Dudley, David Walker, said fears about immigration bore no relation to reality, London's mayor, Boris Johnson, said Cameron was right to stop people "leeching" off the system. Cameron's detailed proposals will require legislation, and are likely to be scrutinised both among his own party to assess just how radical they are and for compatibility with EU law.

Downing Street also promised to strengthen the test people have to pass to see if they are eligible to claim income-related benefits – the so called habitual residence test which ensures that the UK is a person's main residence. There will be an increase in the number and a stronger range and depth of questions asked, the government said.

EU citizens, following previous court rulings, are not currently required to pass the habitual residence test, and there appears to be no plan in the Cameron speech to change this.

No 10 said it was also closing a loophole whereby someone that has worked in the UK and paid national insurance could continue to claim benefits even if they overstayed their visa.

In addition, the government is looking to see how it could stop paying benefits, including child benefit, for children who live in other EU states when their parents are working here.

On the emotive subject of social housing, No 10 promised to impose an expectation on councils to introduce a local residency test in determining who should qualify. This would mean someone would have to live in an area for between two or five years before they could even go on the waiting list.

UK nationals, including armed service personnel, moving from one council area to another will be exempted if they moved for genuine reasons – for example for work or because of family breakdown, such as domestic violence. Ministers are also likely to face a need to make exemptions for the unintentionally homeless, and for asylum seekers.

The Department of Communities has already sent circulars to local councils advising them to put those with a local connection ahead of others in the social housing queue. Many councils do so, and give additional points to those with a strong local connection.

But No 10 said the number of non-UK residents in social housing had risen from 6.5% in 2007 to more than 9% in 2011.

Different research published by the Equality and Human Rights Commission in 2009 found that new migrants in the UK over the previous five years made up less than 2% of those in social housing.

The vast bulk of foreign nationals lived in the private rented sector.

Cameron will also target illegal immigration – doubling the maximum fine for companies that employ illegal workers to £20,000 – and signal action against so-called "health tourism" that could mean non-EU nationals have to prove they hold insurance before getting care.