Media playback is unsupported on your device Media caption Home Secretary Theresa May said the public is asking why illegal immigrants can stay in the UK ''so easily''

Illegal immigrants will find it harder to set up home in the UK under planned laws, says Home Secretary Theresa May.

The Immigration Bill would force private landlords to quiz tenants about their immigration status and restrict access to bank accounts for people in the country without permission.

It also aims to streamline the appeals process in immigration cases.

Labour said the bill did nothing about bigger problems like the "shambolic" state of UK border controls.

The bill, which is expected to become law in spring 2014, subject to approval by MPs, will include measures to allow the UK to "deport foreign criminals first and hear their appeal later" when there is "no risk of serious irreversible harm".

BBC home affairs correspondent Dominic Casciani says this could lead to an increase in air fare costs for the Home Office, if it has to fly back migrants who are successful in their appeal.

A requirement is also included for temporary migrants, such as overseas students, to make a contribution to the National Health Service to prevent so-called "health tourism".

Other new measures in the bill include:

New powers to check driving licence applicants' immigration status

Cut the number of deportation decisions that can be appealed against from 17 to four

Restrict the ability of immigration detainees to apply repeatedly for bail if they have previously been refused it

Make it easier for the Home Office to recover unpaid civil penalties

Clamp down on people who try to gain an immigration advantage by entering into a "sham" marriage or civil partnership

Require banks to check against a database of known immigration offenders before opening bank accounts

Immigration minister Mark Harper said: "The Immigration Bill will 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.

Analysis When you average them out, there's been one immigration bill roughly every two years since 1997 and the system apparently still needs fixing. Each bill has seen a minister take legislation to Parliament and tell MPs that this is the one that will make the system firmer, faster and fairer - or words to that effect. So what makes this latest attempt any different? This bill is almost entirely about enforcement: it focuses on people the government wants to control or keep out. Critics say much of it may prove challenging to implement: landlords will need to become experts in forged passports, there will be new court battles over the appeals process and, undoubtedly, complaints of poor and unfair decisions will remain. The ultimate goal is increased public confidence in the system. Whatever measures are in this bill, that remains the most challenging aim of them all.

"We will continue to welcome the brightest and best migrants who want to contribute to our economy and society and play by the rules. But the law must be on the side of people who respect it, not those who break it."

Mrs May said the measures were about "making it harder for people who are here illegally to stay here".

She said it was a "point of principle" that people who used public services should be expected to contribute to them, but she would not comment on the cost to the country of "health tourism".

She denied claims that forcing private landlords to check the immigration status of prospective tenants would be unworkable, saying they would just be "required to ask some simple questions" in the same way that employers have to do when interviewing workers.

But an organisation representing private and public sector landlords said the measures would "make it much harder for non-British people to access housing even when they have a legal right to live in the UK".

Gavin Smart, director of policy and practice at the Chartered Institute of Housing, said: "Checking immigration status is complicated so landlords may shy away from letting to anyone who appears not to be British."

Don Flynn, director of Migrants' Rights Network, criticised moves to restrict access to the NHS, saying: "There are very small numbers of migrants who come here with pre-existing health conditions and find themselves registering with the health service.

"I simply do not believe there is any significant evidence that something like the NHS is a pull factor."

'Increasingly shambolic'

The British Medical Association (BMA) is also critical of the plans.

Dr Richard Vautrey, deputy chairman of the BMA's GPs committee, told BBC Radio 5live there is already a system in place for hospitals to recover the cost of treating patients who are ineligible for NHS care.

Media playback is unsupported on your device Media caption Liberty's Emma Norton: Judges often apply the law "very harshly"

"Clearly that could be improved, but introducing a system for general practice could be a bureaucratic nightmare," he said.

"The reality is people don't come to the UK to use the NHS, they're more likely to come to work in the NHS."

Labour said there was nothing in the bill to tackle problems at the UK's "increasingly shambolic" border controls or to deal with "long delays in getting electronic checks in place, or the UKBA (UK Border Agency) bureaucratic failings that have prevented foreign criminals being deported".

Shadow home secretary Yvette Cooper told BBC Radio 4's The World at One: "It doesn't seem to address some of the serious issues around border control and some of the problems about exploitation of immigration in the labour market, particularly low-skill immigration, which has caused concerns about jobs and wages."

Campaign group the Joint Council for the Welfare of Immigrants welcomed what it claimed was a "climb down" by the Home Office, which had not included in the bill proposals to introduce immigration checks by GPs.

It said the new proposals would deter students from wanting to study in the UK but would have "no impact whatsoever on 'illegal' immigration - the declared intention of this bill".

UKIP said "pressganging landlords, doctors and private citizens under the threat of sanctions to carry out the work of border agencies is simply wrong" and the government needed to treat the cause of immigration problems rather than the symptoms.

And Simon Walker, of the Institute of Directors, warned that some of the government's rhetoric was starting to make the UK "look unwelcoming and hostile to the people on whom our export markets depend".

The Conservatives say they want to reduce net migration from non-EU countries - the difference between the number of people emigrating and arriving in the UK - to less than 100,000 a year.

But the latest Office for National Statistics figures show net migration rose to 176,000 in the year ending December 2012 - up from 153,000 people in the year to September 2012 - appearing to buck the recent downward trend.

There are no official estimates of the number of illegal immigrants in the UK. A 2009 study by the London School of Economics produced an estimate of 618,000 but the Migration Watch pressure group said this under-estimated the number of people who had overstayed their visas and the true figure was more like 1.1 million.