That assumes all deaths are logged. There are strong financial incentives for relatives to hide a death from the government if it means getting a check every month
It's quite hard to hide a death in the UK. In hospital all deaths are certified, outside of hospital you have the interesting problem of how to deal with the corpse. And in addition to the death register there are also tax filings (including Council Tax, which is a hefty sum and paid monthly), utilities, and other services that require ID.
The media do print occasional Capitalist Gothic stories of people who kept a corpse in their house. But that's incredibly rare and - for obvious reasons - a high price to pay for a monthly cheque.
The government loves spending money on themselves.
So the government thinks it's perfectly reasonable to have 50 FTE spend 5 years on preventing a single false claim. Ideally through the commisioner's brother's company, not directly. This is a necessity!
The media do print occasional Capitalist Gothic stories of people who kept a corpse in their house. But that's incredibly rare and - for obvious reasons - a high price to pay for a monthly cheque.