If you manage to get into the London School of Economics, banks hire directly from there (Goldman Sachs is actually their largest "consumer" of graduates). However you would not necessarily end up in a trading department, they have many other departments from accounting to risk management to legal compliance etc. In any case you would become a very well paid bank employee with an excellent perspective which is not that bad I guess. As for suitable subject to study, talk to the uni.
If you have an apetite for the risks involved and are ready to sacrifice sure salary from an employer go for your own career as described in the other replies here and you will enjoy the privilege of being able to make your own decisions. And, treat your capital carefully, it may grow substantially over the time - remember the magic of compound interest.
Dboy - get into industry or create an app and sell it to Facebook...its the only way to make money now. Finance is not what it is cracked up to be. Having said there are a few people in Dublin now who are looking to set up a new spread betting business....0 spreads on the majors I hear. Be careful what you wish for.
In reply to the above comment we are pleased to inform you that the company London office is based in the centre of the City of London, within a 5-minute walk from the Bank Tube station. With regards to our customers’ experience you are very welcome to watch a recent feedback video here Investment Banking Training Financial Modeling and Valuation - YouTube.
Please consider this post as not an advertising effort but simply an attempt to clarify the facts to the members of this respected forum. Feel free to contact us for any further information.