A degree is not required, nor is a masters or a super-clean school/college academic record - that is perhaps the biggest misconception in young people when it comes to getting a city job. Perhaps if you want to do a graduate scheme yes, but work in the city (as a trader or any other profession) - no.
All you need to do is have an understanding of the business and then be able to newtwork, have persistance and it will come. You have to be extremely proactive may I add; and strong interpersonal skills will get you a long way. You do not need to study or pay for any of this.
In my own situation I went to Uni and now am currently doing an internship at one of the top 3 US IB's, however when it is over I am going home to trade full-time and will make a big effort to network with every prop firm in the city whilst trading (hopefully with some success!) until they can't say no! I make it clear to all I speak to now that I want to trade, be it for myself, an IB or a prop house... by the end of this year it will be my full-time profession.
The alternative to the above route is a 2 year grad scheme, followed by 2-3 years of (trading) floor experience and professional qualifications and then, if it all goes to plan, I might be able to begin trading institutionally. I am not prepared to wait 5-6 years myself.
To acknowledge the above poster if I had a million in my bank I would be off to somewhere exotic tomorrow! I am interested in finding a mentor, turning 1,000 into 10,000 in 6 months is one thing, managing and returning millions is going to be a lot different I imagine but that is where I want to be 5-6 years down the line, not just starting out.