Your Cash Deposit Account is a sub-account of a segregated client account held at the Bank of London. The sub-account is held in your name, containing only your funds, separated and segregated from everyone else's funds. Each month, we receive interest from the bank which is then applied to your account.
High-street banks accept deposits (hold your money) and then make money on that money by lending it out to others (and charging interest to those borrowers). They receive the full Bank of England base rate from your deposits, but that goes towards their operating costs and overheads. They generally pass on only a fraction of that amount to you, the person whose money they are using.
National Savings and Investments (ns&i) is backed by HM Treasury. They are the governmet's savings bank (they were originally the Post Office Savings Bank). When you deposit with them, they lend your money to the Government, so their rates reflect whatever the Government is willing to pay from time to time to borrow money. If the Government can borrow money cheaper (say, from another government), then ns&i will drop their rate so that it remains competitive.
The Bank of England pays its full base rate on all deposits made with it. We deposit your funds at the Bank of London who, in turn, deposit those at the Bank of England. The Bank of London receives the full base rate from the Bank of England, takes a small percentage to cover the cost of its expensive technology and human resources that enable these accounts to even exist, and then passes the rest to us. We take 10% of the interest that comes through, leaving you with 90%.
Ultimately, your money is held unencumbered, in cash, at the Bank of England. It is never loaned out, pledged or otherwise interfered with - it simply sits there. Legally, are we are your bare trustee, our name isn't on your money anywhere. We operate client accounts with the Bank of London, which are opened in your name and contain your funds. Those funds are held by the Bank of London at the Bank of England.