As I see it, as a banker, it's your salary through tax that is going to be paying the salaries of many these doctors to provide care for people who could not realisticially afford it in a private healthcare system. City workers are not pariahs leeching off society; in fact they earn a significant proportion of the wealth that keeps this country afloat, and the public sector workers in work. Don't be pressured out of going into the City because people are telling you it's somehow immoral - that view is simply nonsense.
The thing you have to weigh up is how much you will enjoy the job. For some people, money is really important, for others, having an enjoyable job is more important. That's a decision you have to make. Similarly, for some people work as a doctor is more enjoyable, for others work as a banker is more enjoyable. This, again, is a decision you have to make. Both professions have pretty crap hours. Medicine is difficult to get into the training, difficult to complete the training, difficult to get a job and even more difficult to get a job you want. Banking, on the other hand, seems to be more straightforward to get into, but only if you make the grade, and it is ultra-competitive. Even if you get in, if you don't keep producing at the level the bank wants you will lose your job.
I know people who work in both sectors, and they all enjoy their jobs. It isn't a case of one being better than the other, or more interesting work than the other. Banking is, however, better paid, but you can't give no consideration at all to what the job's going to be like, since you're going to be working 50+ hour weeks by all accounts, and few people can stick that out if they hate the work despite the knowledge of a lot more money to spend doing things in your free time. Also, while banking is better paid, if you go down the banking route but dont get a job in banking (or lose your job), your second, third, etc. choice jobs are not likely to be as well paid as being a doctor over your career.
The bottom line, though, is that both these careers are elite, and highly competitive. If you're only interested in the money you're unlikely to have the dedication to outcompete the 5+ other people of similar standard who want the same job.