This is widely unpopular because the idea of ID cards is unpopular in general in the UK and the people also clearly understand that the argument that this would combat illegal immigration is total rubbish. Even the comments on The Guardian's website are overwhelmingly negative, which should really tell the government something.
The proposal is also drastic because it would be de facto mandatory for all residents. It's hilarious and pathetic to see the government argue that it wouldn't be mandatory, just only needed to get a job (which probably means also mandatory to rent and to study)...
An unpopular government trying to out-do itself.