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Alexander - what most people refer to as 'City Bankers' are running investment funds on which they get a salary plus a bonus reflecting the performance of their fund. These tend to be among the highest paid. Many of them are particularly good at their job and well deserve what they earn, others are less good and dont do much better than track the index, or even do worse, they will earn a bit less but their investors might think they deserve even less than they get!
The ways in which banks make their money is complex ,from which their salaries are paid. These salaries must reflect the market or the bank will not get decent people. Those investment managers that get the results simply wont work for them!
Remember as well that not all banks had a government bail-out and even one of those that did, Lloyds TSB, only needed that bailout because they rescued one of the 'guilty' banks - HBOS, on the personal urging of Gordon Brown.
I do have a bit of sympathy with even the big bad boy, RBS, when they were attacked recently over bonuses, they simply will not get decent people if they don't match the market. Personally the people who were guilty of making the poor management decisions that led to RBS needing a bail-out are the ones that should be singled out and denied bonuses, the others, just doing their job (well) should not be targetted.