Re: Pretty good for public sector IT
"a simple website that allows anyone to tap in their numbers and see what, if anything, they are entitled to."
And send the welfare bill through the roof? The system is designed to make it as difficult as possible to claim what you're entitled to. The last thing the government wants is to give more money to poor people who were previously denied benefits because of some minor error they made on a 156 page application form supplying information the state already has.
If you really want to simplify the benefits system, just give everyone a minimum income of £100 a week. No application form, no means testing, just register on the electoral roll and with HMRC as a UK tax payer. The savings on beauracracy, premises,fraud investigations, appeals, etc would probably cover it. And if you want more, get a job.