The bill, to be introduced in the autumn, will also contain measures against takeaway restaurants and off-licences which employ illegal migrants.
Penalties will also include an unlimited fine and wages being seized.
Immigration Minister James Brokenshire said the government “would continue to crack down on abuse” of the system.
The government has made a series of immigration announcements over the summer of which this is the latest.
Takeaways and off-licences could lose their licences if they were found to be employing illegal workers.
Officials are also considering whether this provision should be extended to cover minicab drivers and operators.
The legal defence for other kinds of business discovered using illegal workers will also change.
They will no longer be able to claim they did not know a particular employee was not allowed to work – they will have to show that they carried out proper checks before taking them on.
The maximum sentence for employers found guilty will be raised from two to five years, in addition to the fines already in force.
Mr Brokenshire said: “Anyone who thinks the UK is a soft touch should be in no doubt – if you are here illegally, we will take action to stop you from working, renting a flat, opening a bank account or driving a car.
“As a one nation government we will continue to crack down on abuse and build an immigration system that works in the best interests of the British people and those who play by the rules.”
Alp Mehmet, of Migration Watch UK, which supports tighter immigration controls, said: “This is not just about not being seen as a soft touch.
“More important is for the message to go out that if you are here illegally and caught working, you and your employer will end up in court.
“Let us hope that the authorities will not shy away from acting on the powers they are to be given, since their record on that front has not always been exemplary.”
Earlier this month, the government also announced that landlords in England will be expected to evict tenants who lose the right to live in the UK, also under the proposed Immigration Bill.
Landlords will be able to end tenancies, sometimes without a court order, when asylum requests fail, and will be required to check a migrant’s status in advance of agreeing a lease. Repeat offenders could face up to five years in prison.
And Mr Brokenshire has previously said businesses that employ illegal workers will be hit with “the full force of government machinery”.
Immigration officers are reported to be preparing to mount a wave of raids this autumn targeting building sites, care homes and cleaning contractors.