Under the Government's centrepiece Immigration Bill, which is introduced today, banks will have to check against a database of known immigration offenders before opening accounts.
Elsewhere, the bill will slash the number of grounds on which migrants can lodge an appeal, from the current 17 to just four - a move drawn up in response to the 12 years it took to deport radical cleric Abu Qatada.
And, as previously disclosed, a new requirement will be introduced for temporary migrants such as overseas students, to make a contribution to the National Health Service.
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.
"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."
Private landlords will be required to check the immigration status of their tenants, to prevent those with no right to live in the UK from accessing private rented housing, while new powers to check driving licence applicants' immigration status will be introduced.
Home Secretary Theresa May and Prime Minister David Cameron want to reduce net migration from non-EU countries to less than 100,000 before the next election in 2015.
Most recent figures from the Office for National Statistics (ONS) showed a net flow of 176,000 migrants came to the UK in the year to December 2012, up from 153,000 in the year to September 2012, ending five consecutive quarters of decline.
Shadow immigration minister David Hanson said the legislation would do nothing to tackle "increasingly shambolic" border controls.
He said: "The Tories are still failing on immigration and this Bill won't address some of the biggest problems.
"The number of foreign criminals deported has dropped by over 13% since the election, border checks have been cut with only half as many people stopped and illegal immigration has got worse.
"Yet there seems to be nothing in the promised Bill to tackle problems at border control, which is getting increasingly shambolic, nor deal with long delays in getting electronic checks in place, or the UKBA bureaucratic failings that have prevented foreign criminals being deported.
"Nor are they tackling exploitation in the labour market which raises greatest public concern. For example the Bill is an opportunity to tackle problems such as enforcement of the minimum wage which would respond to concerns about the impact of EU migration.
"Theresa May has a history of promising big and pretending all is well, but the Government is continuing to fail on immigration policy. This Government is still failing on immigration even on its own measures, with net migration now going up again rather than being in the tens of thousands as the Prime Minister promised."
Shami Chakrabarti, director of human rights group Liberty, said: "After the racist van stunt, the Home Office again scrapes the barrel by turning landlords into immigration officers and scrapping appeal rights for the vulnerable.
"Once more headline-grabbing gimmicks trump tackling departmental delays, and public fears are stoked instead of calmed by putting the house in order.
"Fair and legitimate immigration rules have their place but this nasty Bill is a race relations nightmare waiting to happen."
Mrs May said landlords who rent out property without running the proper checks will be fined and a helpline will be available to check on prospective tenants.
She said the helpline will run in the same way as a current helpline employers can use to check applicants' status.
And she said the NHS, which "has always been quite bad at" charging, will bill immigrants for using the service.
The Home Secretary told BBC Breakfast: "We will be asking for a surcharge, there will be a sort of levy on people who are going to be coming here, to be staying for a while, to contribute so people can feel it is fair...
"One of the things the NHS has always been quite bad at is charging people who they should be charging, people who don't have the right to free access to the NHS and recovering those costs from them."