I hate to sound cynical but this threat isn't aimed at, how do I put this delicately, 'white collar' people.

The government is trying to track down the poorer labourers who have been here for years and years without any sponsorship and illegally.

Ideally you should be carrying on your person your ID card, but if you aren't I am sure they will let you provide it.  The people who should be worried aren't the sorts of people posting on this blog, but the poorer Asian workers living here illegally.