The government doesn't know everyone's financial situation on a day by day basis.
You could combine the tax and benefits systems, but even that only gives a partial picture. They don't know immediately if a couple move in together, or separate, they don't know how much a self-employed person is earning until they put in a tax return, etc.
So, while they can look at past years, and take a sample, and work out roughly how many people they would expect to claim, they can't pro-actively identify everyone who is eligible.
As well as advertising/info campaigns, governments and local councils will employ people to actively try and locate those not claiming, but it's more a case of going out and talking to pensioners about their living situations, rather than just looking it all up on a computer.