The crackdown on immigrants is just an excuse. The real reason is different, the government is out of money and it doesn't believe most of the current welfare bill goes to people in genuine need. (Hence why the previous misadventures of a left-wing government involved 2 attempts at cutting welfare - first the winter bonus for pensioners, then a type disability payments).

The direct attempts at a crackdown failed, and the civil service keeps telling them it can't find any welfare fraud, (which looks fairly unlikely, given certain regional patterns), so they are trying to attack the problem indirectly - by synchronizing the identity numbers of different government record-keeping systems - HMRC, national insurance, the NHS, the land registry, council records.