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.
More top news
Tesco recalls own-brand squash after customers complain of "disgusting taste" and parents worry it may have caused children's stomach upset.
Bradford City co-chairman Mark Lawn has blasted TV broadcasters over their FA Cup fifth round match choices
Face to face with 2 tons of unpredictable muscle is an awe-inspiring moment but within a few years it will be impossible, they will be gone.