The proposed law is at the heart of the push by Prime Minister David Cameron's centre-right Conservatives to create a "hostile environment" for people not authorised to be in the country.
Under the proposed measures, British landlords could be jailed for up to five years if they rent property to people they know or have reasonable grounds to suspect of being illegal immigrants.
Other measures include potential six-month jail terms for people who work illegally, allowing police to seize their wages as "proceeds of crime" and making it a legal requirement for certain public sector workers to speak fluent English.
Cameron's party secured a surprise victory in May's general election with a manifesto which made reducing immigration one of its central themes.
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Net migration to Britain was estimated at 330,000 in the year to March -- the highest figure on record -- and the Conservatives want to cut this to tens of thousands annually.
The main opposition Labour party, led by left-winger Jeremy Corbyn, says the bill could signal the return of the kind of discrimination faced by immigrants to Britain in the 1960s when they sought accommodation.
"By being more insidious, such casual discrimination will be far harder to challenge."
The Joint Council for the Welfare of Immigrants campaign group said the measures would increase "the fear and hostility felt by those who appear different," who would "find it more difficult to live in the UK".
While Tuesday's debate is the first chance MPs have to discuss the bill, it is likely to take months to pass through parliament before becoming law.