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
Largely dry elsewhere tonight with a widespread frost and icy stretches
The so-called mini-Beast from the East has swept in, bringing with it snow, ice and strong winds.