I work in financial services - I won't say where, I'm quite a private person.
The following information is accurate, but the press seem totally unable to grasp it so this might be the first time you've heard it explained...
They make money from "normal" accounts. These are accounts with a turnover of 1000 to 3000 per month. These accounts pay direct debits, card transactions, may have an overdraft, may have a credit balance. Banks like these accounts and can offer you a good service, while not charging you directly. Everybody wins with these accounts.
Banks still make money from "low" accounts. By normal I mean turnover of 400 to 1000 a month. Those accounts generate profit from card transaction fees (retailers pay these), and by using the small credit balances in the accounts. Overdrafts at standard rates (roughly 20%) are
not profitable because of the risk profile. Overdraft charges on those who exceed their limits make these accounts profitable.
Banks do not make money on accounts for people on benefits - "basic "accounts with a turnover of less than 400 a month, for the bulk of these accounts. They do make money from overdraft charges, but overdraft interest in itself is not enough to cover the risk. The card transactions and credit balances generally are not enough to cover account administration.
If banks are prevented from charging overdraft fees then it changes the marketplace quite considerably.
"Normal" accounts will still be in heavy demand by banks.
"low" accounts will not see much in the way of overdraft facilities, and banks will not compete for these actively. They may even attempt to get rid of them, or make them profitable by charging a monthly fee.
"basic" accounts will have customer service sliced to the bone, will not feature overdrafts, and are very likely to be charged for
Overdrafts will still be for the majority of people, especially joint accounts. But for young single people they can forget it, and for poor people they're just going to get the rough end of the stick.
Banks are already, and have been for a while, trying to tier the services they offer. They are attempting to divide their customer base into levels, so that they can offer a different level of service to different customer tiers. Essentially if you don't make the bank money then they will not want to speak to you.
Previously bank charges on "normal" accounts have been a bonus for banks. They didn't need them to make a profit on these accounts, but they got them anyway.
On lower turn over accounts these overdrafts fees are pretty much required in order to avoid them being loss making accounts overall. Essentially those dumb enough to run their accounts badly subsidise the system for those who do not. Without this subsidy then poor people can forget any hope of having decent banking facilities.
Banks lend in three distinct ways for unsecured (in most cases secured lending is a mortgage, or a loan against a house) lending. Overdrafts I've already mentioned.
Personal loans... Previously they were too lax and banks were handing out cash right left and centre. All of a sudden the credit crunch hits, the personal debt bubble bursts etc. As a result many personal loans are not repaid. An additional hurt to the banks is the ultra high profit payment protection insurance industry has been virtually wiped out, this insurance partly subsidised personal loans. Banks face higher bad debts on personal loans than they had expected. However personal loans that are now agreed are much less profitable for the banks, but they are taking much less risk. However debt laws in the UK are still forcing APRs up. Banks use "risk based pricing" which simply means that if they believe you are a higher risk than average they will charge you a higher rate, rather than just say no.
Credit cards are a slightly different story. Similar to personal loans there is risk based pricing. A credit card makes a profit from card transactions, and from interest. Previously there was also a huge amount of profit made from credit card charges similar to overdraft charges. This was capped at £12, cutting into profits. When that happened banks slightly increased costs on other charges on the cards, but the big change was simply taking the cards or limits away from higher risk people. The risk was no longer subsidised by charges, so the banks decided not to provide a loss making service.
A major problem in the UK is our debt laws. They are far, far too soft. They were needed, to help people get round where financial institutions were simply throwing credit around. That's no longer the case, but the law is still the way it is.
Essentially many people can suddenly decide to stop paying their creditors. Financial institutions then typically are arm-twisted into stopping charging interest, cutting parts of the debt away, selling it at a huge discount to debt collectors, or writing the debt off. This does mean that people who need help are being helped. It also means that those of us who pay our debts off also have to pay for those that get out of it. This means we all pay more interest, because of risk, than we should be paying.