You fail at banking....
What difference is it to the bank if they are paying 4% interest on 1000 accounts with £500 in or one account with £500,000? It all adds up to the same amount.
The savings help pay for the loans side of the business, the more cash they have in savings the less it costs them to give out loans, allow credit cards etc. Banks like having lots of saving customers, it means they don't need to borrow money to finance their debtors, like for example Northern Rock...
I fail at banking....I beg to differ

I've got a degree in Accounting & Finance and have spent the last ten years working in Banking, the last five as a Senior Officer in the Treasury of one of the largest building societies in the country.
A lot of customers with £500 each is actually less profitable than one customer with £500,000 - one customer with £500k is less likely to withdraw all that much in one go, meaning the bank can tie it up in loans on the wholesale/credit markets for longer, and actually earn more interest (if the yield curve is positive.) A lot of customers with small balances means there is more chance of large withdrawals all in one go, meaning cash can only be tied up for shorter periods, earning less interest. It's easier to predict customer behavior for one high value customer than lots of small value customers.
It's obviously not that simple though!
As has been said, savings are used to finance loans and credit which are much more profitable than the savings themselves.
For example, a bank might pay you 5% interest, but it will take your money and lend it out on, say, a credit card at something like typically 16% interest or more.
That portion it doesn't lend out in credit goes on the wholesale market, which will earn little more than that 5%. For example in August/September the LIBOR rate was around 5.8% which was quite high - it's lower now that rates have fallen and the spread to the BoE Repo rate has fallen - meaning that back then the bank makes just 0.8% on that 5% savings account, and that's before deductions for operating expenses etc. Of course it depends on the T&Cs of the account and the rate etc etc etc....
All these banks eg HSBC and Lloyds offering 8% on savings are making little to no money on those accounts (and may well be running at a loss) - they get you by tying you to their current accounts on which they pay didly interest but they get your "current" cash to lend out, and that's where the profit comes from.
Also, a lot (sometimes all) of the savings rates are swapped using interest rate swaps, but that's a whole other story
