Former shadow public health minister Diane Abbott dubbed new immigration legislation "a nasty little bill" and warned it would demonise British people of colour.
Some plans were already covered by British law, such as preventing illegal immigrants from getting NHS care, she told Daybreak.
"If the Government wanted to help with that it could help hospitals collect the money," she added.
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The new measures would mirror childcare vouchers and see workers sacrifice some of their salary to benefit.
Google, Facebook and Twitter could face multi-million pound fines over their failure to remove illegal content, MPs say.
Staffing levels and worsening pay are to blame, according to the report by the Health Foundation.