Unveiling the Government's highly-anticipated Immigration Bill, ministers said the new changes will stop migrants abusing public services, deter illegal immigrants from coming to the UK and make it easier to remove people who should not be here.
Key measures in the Bill will see temporary migrants, such as overseas students, pay to access the NHS in an attempt to tackle so-called "health tourism", while the appeals process against deportation is to be streamlined.
Banks will be forced to carry out background checks to stop illegal immigrants opening accounts, while applicants for a driving licence would also have to prove they were in Britain legally.
The Opposition said the Bill would do nothing to tackle "increasingly shambolic" border controls, while campaigner Liberty said the new laws were a "race relations nightmare waiting to happen".
Liberty director Shami Chakrabarti 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.
"Fair and legitimate immigration rules have their place but this nasty Bill is a race relations nightmare waiting to happen."
Maurice Wren, chief executive of the Refugee Council, a UK charity which works directly with refugees and asylum seekers, said: "The Refugee Council is extremely concerned that some of the measures reported to be in the Immigration Bill will have detrimental and unintended consequences - penalising asylum seekers and refugees who have a legal right to live in the UK.
"Requiring landlords and banks to check people's immigration status is simply unworkable. Landlords and bank staff are not immigration officials and the types of documentation carried by asylum seekers and refugees is varied and complex."
Under the Bill, the number of grounds on which migrants can lodge an appeal are to be slashed from the current 17 to just four in a move drawn up in response to the 12 years it took to deport radical cleric Abu Qatada.
It will also aim to curb the number of migrants who block deportation using Article 8 of the European Convention on Human Rights - the right to a private or family life.
Temporary migrants will have to pay a health surcharge as a precondition of entering the UK, to allow them to access free NHS care to the same extent as a permanent resident.
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.
Bank managers will be forced to check potential customers against a database of foreigners known to be in the country illegally, while employers will face heavier fines if they take on staff who have no right to work in the UK.
Shadow immigration minister David Hanson said the Bill will not address some of the biggest problems linked to immigration.
He said: "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 UK Border Agency bureaucratic failings that have prevented foreign criminals being deported."
An immigration bill has been introduced in the UK on average every two years since 1997.
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.
It has been suggested the Government's tough approach to immigration is partly in response to a surge in popularity for the UK Independence Party (Ukip), which campaigns heavily on the issue.
Unveiling the Bill, Immigration Minister Mark Harper said: "The UK has a long and proud history of immigration. Our immigrant communities are a fundamental part of who we are and we are a richer and stronger society because of them.
"But the public expects and deserves an immigration system that is fair to British citizens and legitimate immigrants and tough on those who abuse the system and flout the law.
"The Immigration Bill will stop migrants abusing public services to which they are not entitled, reduce the pull factors which draw illegal immigrants 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."
The Government expects measures in the Bill to be implemented from summer 2014 onwards.
Paul Oakley, Ukip European Parliament candidate in London, likened the Government's focus to "trying to put toothpaste back in the tube".
Mr Oakley, a barrister, said: "Pressganging landlords, doctors and private citizens under the threat of sanctions to carry out the work of border agencies is simply wrong.
"The problem of immigration needs to be prevented, rather than what the Government are doing, which is treating the symptoms not the cause."
Health charity Doctors of the World said it was concerned by the proposals in the Bill to charge for access to healthcare for migrants.
Leigh Daynes, executive director of Doctors of the World UK, said: "It's right that those who can pay should pay if they are not entitled to free healthcare.
"But there is no credible evidence of rampant 'health tourism' to the UK. Migrants don't come here to see a dentist. They come to work and provide for their families, or to seek protection from persecution.
"We know from our London walk-in clinic that more and more migrants living here are being refused treatment even though entitlement rules haven't changed."
Commenting on proposals aimed at banks, a spokesman for the British Bankers' Association (BBA), which represents the banking and financial services sector, said: "We will work with the Government and examine the details of these proposals to ensure they are legally sound, fair and effective."