There's no "simple" answer to this one mainly because there's no straightforward definition of "an accountant". People usually mean "Chartered Accountant" when they refer to an accountant and the usual way to qualify as one of those is to go to University, get a degree (not necessarily an accountancy one but it helps), get a training contract with an accountancy firm and then undertake three years training "in firm" whilst taking exams along the way. From leaving school it's probably a 7 year process.
The ICAEW and ICAS these days have opened up routes to qualify without a University degree by going straight into work and doing college classes etc from there but it's a longer route and in my opinion far more difficult. Personally I wouldn't recommend it but I guess Miss-taken's advice in that area is more relevant as she went that route and did so more recently than me (I went the Uni degree route).
Quite apart from all this, the main Chartered bodies don't have a monopoly on the term "accountant". You can train with ACCA as a "certified" or with CIMA/CIPFA etc. Indeed you can train with nobody at all and still call yourself "accountant". Unlike lawyer, and much to most accountant's annoyance, the term "accountant" is not protected. Nothing to stop a 16 year old straight out of school advertising their services as an "accountant" if they wish (though they can't claim to be a "Chartered Accountant").
In contrast to Ethel's first post, you would probably find if you can get a job with an accountancy firm that they would be quite happy to send you down the training route for qualification without a degree. It's a good way of encouraging staff really and if they don't make it through they probably benefit from the experience without the firm having to pay them significantly more than they do any other "clerk". If they do make it through, so much the better.