What, everybody's accounts, millions of them, all sent to the Treasury, every year? I don't think so! Individuals are obliged now to inform HMRC only if they make over £1000 in interest, which won't apply to most people. Banks do have your NI number, and so I suppose they can keep a list of big spenders or big savers, but the obligation is on the taxpayer to do their own sums and submit their figures if they have a tax liability.
I am currently sorting out the estate of a deceased elderly relative who had loads of different savings accounts. I wish with all my heart that somebody other than me could have traced and claimed all the money due to the estate, but it was entirely up to the other executor and me. There is no central record of these things, more's the pity. HMRC knew what tax had been deducted from her savings interest, but that's all. They don't know what the actual interest rates were or what her total assets were, or what money went in and out of the accounts, or where it all came from or went to.